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Artykuły w czasopismach na temat „Matching”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

CHENG, EDDIE, and SACHIN PADMANABHAN. "MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR CROSSED CUBES." Parallel Processing Letters 22, no. 02 (2012): 1250005. http://dx.doi.org/10.1142/s0129626412500053.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In thi

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MAO, YAPING, and EDDIE CHENG. "A Concise Survey of Matching Preclusion in Interconnection Networks." Journal of Interconnection Networks 19, no. 03 (2019): 1940006. http://dx.doi.org/10.1142/s0219265919400061.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. There are other related parameters and generalization including the strong matching preclusion number, the conditional matching preclusion number, the fractional matching preclusion number, and so on. In this survey, we give an introduction on the general topic of matching preclusion.

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3

Chen, Ciping. "Matchings and matching extensions in graphs." Discrete Mathematics 186, no. 1-3 (1998): 95–103. http://dx.doi.org/10.1016/s0012-365x(97)00182-9.

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LÜ, HUAZHONG, and TINGZENG WU. "Fractional Matching Preclusion for Restricted Hypercube-Like Graphs." Journal of Interconnection Networks 19, no. 03 (2019): 1940010. http://dx.doi.org/10.1142/s0219265919400103.

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The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, whic

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Echenique, Federico, SangMok Lee, Matthew Shum, and M. Bumin Yenmez. "Stability and Median Rationalizability for Aggregate Matchings." Games 12, no. 2 (2021): 33. http://dx.doi.org/10.3390/g12020033.

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We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching data in revealed preference theory. We present a result on rationalizing a matching data as the median stable matching.

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6

Cannas, Massimo, and Emiliano Sironi. "Optimal Matching with Matching Priority." Analytics 3, no. 1 (2024): 165–77. http://dx.doi.org/10.3390/analytics3010009.

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Matching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important to reduce the number of drops to avoid unsatisfactory results. Greedy matching algorithms may not reach the maximum matching size, thus dropping more units than necessary. Optimal matching algorithms do ensure a maximum matching size, but they implicitly assume that all units have the same matching

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7

Wang, Xia, Tianlong Ma, Jun Yin, and Chengfu Ye. "Fractional matching preclusion for radix triangular mesh." Discrete Mathematics, Algorithms and Applications 11, no. 04 (2019): 1950048. http://dx.doi.org/10.1142/s1793830919500484.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of [Formula: see text], denoted by

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8

Anantapantula, Sai, Christopher Melekian, and Eddie Cheng. "Matching Preclusion for the Shuffle-Cubes." Parallel Processing Letters 28, no. 03 (2018): 1850012. http://dx.doi.org/10.1142/s0129626418500123.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. A graph is maximally matched if its matching preclusion number is equal to its minimum degree, and is super matched if the matching preclusion number can only be achieved by deleting all edges incident to a single vertex. In this paper, we determine the matching preclusion number and classify the optimal matching preclusion sets for the shuffle-cube graphs, a variant of the well-known hypercubes.

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9

CHENG, EDDIE, RANDY JIA, and DAVID LU. "MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR AUGMENTED CUBES." Journal of Interconnection Networks 11, no. 01n02 (2010): 35–60. http://dx.doi.org/10.1142/s0219265910002726.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those incident to a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those incident to a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In t

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10

Ma, Tianlong, Yaping Mao, Eddie Cheng, and Jinling Wang. "Fractional Matching Preclusion for (n, k)-Star Graphs." Parallel Processing Letters 28, no. 04 (2018): 1850017. http://dx.doi.org/10.1142/s0129626418500172.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu introduced the concept of fractional matching preclusion number in 2017. The Fractional Matching Preclusion Number (FMP number) of G is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The Fractional Strong Matching Preclusion Number (FSMP number) of G is the minimum number of vertices and/or edges whose deletion leaves the resulting

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11

Greinecker, Michael, and Christopher Kah. "Pairwise Stable Matching in Large Economies." Econometrica 89, no. 6 (2021): 2929–74. http://dx.doi.org/10.3982/ecta16228.

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We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely to limits of stable matchings for finite‐agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stab

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12

Zhang, Shuangshuang, Yuzhi Xiao, Xia Liu, and Jun Yin. "A Short Note of Strong Matching Preclusion for a Class of Arrangement Graphs." Parallel Processing Letters 30, no. 01 (2020): 2050001. http://dx.doi.org/10.1142/s0129626420500012.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The strong matching preclusion is a well-studied measure for the network invulnerability in the event of edge failure. In this paper, we obtain the strong matching preclusion number for a class of arrangement graphs and categorize their the strong matching preclusion set, which are a supplement of known results.

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13

He, Jinghua, Erling Wei, Dong Ye, and Shaohui Zhai. "On perfect matchings in matching covered graphs." Journal of Graph Theory 90, no. 4 (2018): 535–46. http://dx.doi.org/10.1002/jgt.22411.

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14

Kolupaev, Dmitriy, and Andrey Kupavskii. "Erdős matching conjecture for almost perfect matchings." Discrete Mathematics 346, no. 4 (2023): 113304. http://dx.doi.org/10.1016/j.disc.2022.113304.

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15

Khalashi Ghezelahmad, Somayeh. "On matching integral graphs." Mathematical Sciences 13, no. 4 (2019): 387–94. http://dx.doi.org/10.1007/s40096-019-00307-7.

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Abstract The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs on eight vertices whose matching polynomials have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We show that there are exactly two matching integral graphs on eight vertices.

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16

CHENG, EDDIE, DAVID LU, and BRIAN XU. "STRONG MATCHING PRECLUSION OF PANCAKE GRAPHS." Journal of Interconnection Networks 14, no. 02 (2013): 1350007. http://dx.doi.org/10.1142/s0219265913500072.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. In this paper, we examine the properties of pancake graphs by finding its strong matching preclusion number and categorizing all optimal solutions.

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17

BONNEVILLE, PHILIP, EDDIE CHENG, and JOSEPH RENZI. "STRONG MATCHING PRECLUSION FOR THE ALTERNATING GROUP GRAPHS AND SPLIT-STARS." Journal of Interconnection Networks 12, no. 04 (2011): 277–98. http://dx.doi.org/10.1142/s0219265911003003.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem and has recently been introduced by Park and Ihm.15 In this paper, we examine properties of strong matching preclusion for alternating group graphs, by finding their strong matching preclusion numbers and categorizing all optimal solutions. More importantly, we prove a general result on taking a Cartesian product of a graph with K2 (an edge) to obtai

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18

CHENG, EDDIE, and OMER SIDDIQUI. "Strong Matching Preclusion of Arrangement Graphs." Journal of Interconnection Networks 16, no. 02 (2016): 1650004. http://dx.doi.org/10.1142/s0219265916500043.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph with neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of the star graphs and alternating group graphs, and to provide an even richer class of interconnection networks. In this paper, the goal is to find the strong matching preclusion number of arrangement graphs and to categorize all optimal strong

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19

Faenza, Yuri, and Telikepalli Kavitha. "Quasi-Popular Matchings, Optimality, and Extended Formulations." Mathematics of Operations Research 47, no. 1 (2022): 427–57. http://dx.doi.org/10.1287/moor.2021.1139.

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Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors in a strict order of preference. A matching [Formula: see text] in [Formula: see text] is popular if [Formula: see text] does not lose a head-to-head election against any matching. Popular matchings generalize stable matchings. Unfortunately, when there are edge costs, to find or even approximate up to any factor a popular matching of minimum cost is NP-hard. Let [Formula: see text] be the cost of a min-cost popular matching. Our goal is to efficiently compute a matching of cost at m

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20

Noureen, Sadia, and Bhatti Ahmad. "The modified first Zagreb connection index and the trees with given order and size of matchings." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 13, no. 2 (2021): 85–94. http://dx.doi.org/10.5937/spsunp2102085n.

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A subset of the edge set of a graph G is called a matching in G if its elements are not adjacent in G. A matching in G with the maximum cardinality among all the matchings in G is called a maximum matching. The matching number in the graph G is the number of elements in the maximum matching of G. This present paper is devoted to the investigation of the trees, which maximize the modified first Zagreb connection index among the trees with a given order and matching number.

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21

Juan, Miguel J. Bawagan. "A Kidney Exchange Matching Application Using the Blossom and Hungarian Algorithms for Pairwise and Multiway Matching." Indian Journal of Science and Technology 13, no. 2 (2020): 229–47. https://doi.org/10.17485/ijst/2020/v13i02/149446.

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Abstract <strong>Background/objectives:</strong> Patients of kidney failure sometimes have incompatible donors. This study proposes an application to get the best matchings based on scoring data. <strong>Methods:</strong> For pairwise matching, we created a new graph from the original scoring matrix. This graph ensures pairwise matchings. To find an optimal matching, we used the Blossom algorithm. For multiway matching, we interpreted the scoring matrix as an assignment problem. For this, we used the Hungarian algorithm. The application was created using Python, NetworkX, NumPy, and

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22

Reny, Philip J. "Efficient Matching in the School Choice Problem." American Economic Review 112, no. 6 (2022): 2025–43. http://dx.doi.org/10.1257/aer.20210240.

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Stable matchings in school choice needn’t be Pareto efficient and can leave thousands of students worse off than necessary. Call a matching μ priority-neutral if no matching can make any student whose priority is violated by μ better off without violating the priority of some student who is made worse off. Call a matching priority-efficient if it is priority-neutral and Pareto efficient. We show that there is a unique priority-efficient matching and that it dominates every priority-neutral matching and every stable matching. Moreover, truth-telling is a maxmin optimal strategy for every studen

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23

Pálvölgyi, Dömötör. "Partitioning to three matchings of given size is NP-complete for bipartite graphs." Acta Universitatis Sapientiae, Informatica 6, no. 2 (2014): 206–9. http://dx.doi.org/10.1515/ausi-2015-0004.

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Abstract We show that the problem of deciding whether the edge set of a bipartite graph can be partitioned into three matchings, of size k1, k2 and k3 is NP-complete, even if one of the matchings is required to be perfect. We also show that the problem of deciding whether the edge set of a simple graph contains a perfect matching and a disjoint matching of size k or not is NP-complete, already for bipartite graphs with maximum degree 3. It also follows from our construction that it is NP-complete to decide whether in a bipartite graph there is a perfect matching and a disjoint matching that co

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24

Demuynck, Thomas, and Umutcan Salman. "On the revealed preference analysis of stable aggregate matchings." Theoretical Economics 17, no. 4 (2022): 1651–82. http://dx.doi.org/10.3982/te4723.

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Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable and nontransferable utility and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalizable. For matchings that are not rationalizable, we provide a simple greedy algorithm that computes the minimum number of matches that need to be removed to obtain a rationalizable mat

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25

WANG, YANCHUN, WEIGANG SUN, JINGYUAN ZHANG, and SEN QIN. "ON THE CONDITIONAL MATCHING OF FRACTAL NETWORKS." Fractals 24, no. 04 (2016): 1650054. http://dx.doi.org/10.1142/s0218348x16500547.

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In this paper, we propose a new matching (called a conditional matching), where the condition refers to the matching of the new constructed network which includes all the nodes in the original network. We then enumerate the conditional matchings of the new network and prove that the number of conditional matchings is just the product of degree sequences of the original network. We choose two families of fractal networks to show our obtained results, including the pseudofractal network and Cayley tree. Finally, we calculate the entropy of the conditional matchings on the considered networks and

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26

de Fez, M. D., P. Capilla, M. J. Luque, J. Pérez-Carpinell, and J. C. del Pozo. "Asymmetric colour matching: Memory matching versus simultaneous matching." Color Research & Application 26, no. 6 (2001): 458–68. http://dx.doi.org/10.1002/col.1066.

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Alishahi, Meysam, and Hajiabolhassan Hossein. "On the Chromatic Number of Matching Kneser Graphs." Combinatorics, Probability and Computing 29, no. 1 (2019): 1–21. http://dx.doi.org/10.1017/s0963548319000178.

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AbstractIn an earlier paper, the present authors (2015) introduced the altermatic number of graphs and used Tucker’s lemma, an equivalent combinatorial version of the Borsuk–Ulam theorem, to prove that the altermatic number is a lower bound for chromatic number. A matching Kneser graph is a graph whose vertex set consists of all matchings of a specified size in a host graph and two vertices are adjacent if their corresponding matchings are edge-disjoint. Some well-known families of graphs such as Kneser graphs, Schrijver graphs and permutation graphs can be represented by matching Kneser graph

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28

Doval, Laura. "Dynamically stable matching." Theoretical Economics 17, no. 2 (2022): 687–724. http://dx.doi.org/10.3982/te4187.

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I introduce a stability notion, dynamic stability, for two‐sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one‐to‐one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent's payoff from remaining unmatched cannot be defined independently of other contemporaneous agents'

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CHENG, EDDIE, and LÁSZLÓ LIPTÁK. "CONDITIONAL MATCHING PRECLUSION FOR (n,k)-STAR GRAPHS." Parallel Processing Letters 23, no. 01 (2013): 1350004. http://dx.doi.org/10.1142/s0129626413500047.

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The matching preclusion number of an even graph G, denoted by mp (G), is the minimum number of edges whose deletion leaves the resulting graph without perfect matchings. The conditional matching preclusion number of an even graph G, denoted by mp 1(G), is the minimum number of edges whose deletion leaves the resulting graph with neither perfect matchings nor isolated vertices. The class of (n,k)-star graphs is a popular class of interconnection networks for which the matching preclusion number and the classification of the corresponding optimal solutions were known. However, the conditional ve

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30

Lo, Allan. "Existences of rainbow matchings and rainbow matching covers." Discrete Mathematics 338, no. 11 (2015): 2119–24. http://dx.doi.org/10.1016/j.disc.2015.05.015.

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Hosseini, Hadi, Zhiyi Huang, Ayumi Igarashi, and Nisarg Shah. "Class Fairness in Online Matching." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 5 (2023): 5673–80. http://dx.doi.org/10.1609/aaai.v37i5.25704.

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We initiate the study of fairness among classes of agents in online bipartite matching where there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online and must be matched irrevocably upon arrival. In this setting, agents are partitioned into a set of classes and the matching is required to be fair with respect to the classes. We adopt popular fairness notions (e.g. envy-freeness, proportionality, and maximin share) and their relaxations to this setting and study deterministic and randomized algorithms for matching indivisible items (leadin

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Li, Hong-Hai, and Yi-Ping Liang. "On the k-matchings of the complements of bicyclic graphs." Discrete Mathematics, Algorithms and Applications 10, no. 02 (2018): 1850016. http://dx.doi.org/10.1142/s1793830918500167.

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A matching of a graph [Formula: see text] is a set of pairwise nonadjacent edges of [Formula: see text], and a [Formula: see text]-matching is a matching consisting of [Formula: see text] edges. In this paper, we characterize the bicyclic graphs whose complements have the extremal number of [Formula: see text]-matchings for all [Formula: see text].

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Etesami, S. Rasoul, and R. Srikant. "Decentralized and Uncoordinated Learning of Stable Matchings: A Game-Theoretic Approach." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 22 (2025): 23160–67. https://doi.org/10.1609/aaai.v39i22.34481.

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We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner, where ``decentralized" means that players make decisions individually without the influence of a central platform, and ``uncoordinated" means that players do not need to synchronize their decisions using pre-specified rules. First, we provide a game formulation for this problem with known preferences, where the set of pure Nash equilibria (NE) coincides with the set of stable matchings, and mixed NE can be rounded to a stable matching. Then, we show that for hierarchical m

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Akin, Sumeyra. "Matching with floor constraints." Theoretical Economics 16, no. 3 (2021): 911–42. http://dx.doi.org/10.3982/te3785.

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Floor constraints are a prominent feature of many matching markets, such as medical residency, teacher assignment, and military cadet matching. We develop a theory of matching markets under floor constraints. We introduce a stability notion, which we call floor respecting stability, for markets in which (hard) floor constraints must be respected. A matching is floor respecting stable if there is no coalition of doctors and hospitals that can propose an alternative matching that is feasible and an improvement for its members. Our stability notion imposes the additional condition that a coalitio

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35

Erdős, Péter L., Shubha R. Kharel, Tamás Róbert Mezei, and Zoltán Toroczkai. "New Results on Graph Matching from Degree-Preserving Growth." Mathematics 12, no. 22 (2024): 3518. http://dx.doi.org/10.3390/math12223518.

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The recently introduced model in S. R. Kharel et al.’s study [Degree-preserving network growth. Nature Physics 2022, 18, 100–106] uses matchings to insert new vertices of prescribed degrees into the current graph of an ever-growing graph sequence. The process depends both on the size of the largest available matching, which is the focus of this paper, as well as on the actual choice of the matching. Here, we first show that the question of whether a graphic degree sequence, extended with a new degree 2δ, remains graphic is equivalent to the existence of a realization of the original degree seq

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36

Chen, Jiehua, Piotr Skowron, and Manuel Sorge. "Matchings under Preferences: Strength of Stability and Tradeoffs." ACM Transactions on Economics and Computation 9, no. 4 (2021): 1–55. http://dx.doi.org/10.1145/3485000.

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We propose two solution concepts for matchings under preferences: robustness and near stability . The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for

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Amir, Amihood, Eran Chencinski, Costas Iliopoulos, Tsvi Kopelowitz, and Hui Zhang. "Property matching and weighted matching." Theoretical Computer Science 395, no. 2-3 (2008): 298–310. http://dx.doi.org/10.1016/j.tcs.2008.01.006.

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Nguyen, Thành, and Rakesh Vohra. "Near-Feasible Stable Matchings with Couples." American Economic Review 108, no. 11 (2018): 3154–69. http://dx.doi.org/10.1257/aer.20141188.

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The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a “nearby” instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two. (JEL C78, D47, I11, J41, J44)

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39

Huang, Chao. "Stable matching: An integer programming approach." Theoretical Economics 18, no. 1 (2023): 37–63. http://dx.doi.org/10.3982/te4830.

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This paper develops an integer programming approach to two‐sided many‐to‐one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that a stable matching exists in a discrete matching market when the firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.

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WANG, XIUMEI, WEIPING SHANG, YIXUN LIN, and MARCELO H. CARVALHO. "A CHARACTERIZATION OF PM-COMPACT CLAW-FREE CUBIC GRAPHS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (2014): 1450025. http://dx.doi.org/10.1142/s1793830914500256.

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The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. This paper characterizes claw-free cubic graphs whose 1-skeleton graphs of perfect matching polytopes have diameter 1.

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Gong, Luozhong, and Weijun Liu. "The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number." Journal of Mathematics 2022 (May 28, 2022): 1–8. http://dx.doi.org/10.1155/2022/3589448.

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The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as M G x = ∑ k = 0 n / 2 − 1 k m G , k x n − 2 k , where m G , k is the number of the k matchings of G . Let λ 1 G denote the largest matching root of the graph G . In this paper, among the unicyclic graphs of order n , we present the ordering of the unicyclic graphs with matching number 2 according to the λ 1 G values for n ≥ 11 and also determine the graphs with the first and second largest λ 1 G values with matching number 3.

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LI, YALAN, CHENGFU YE, MIAOLIN WU, and PING HAN. "Fractional Matching Preclusion for Möbius Cubes." Journal of Interconnection Networks 19, no. 04 (2019): 1950007. http://dx.doi.org/10.1142/s0219265919500075.

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Let F be an edge subset and F′ a subset of vertices and edges of a graph G. If G − F and G − F′ have no fractional perfect matchings, then F is a fractional matching preclusion (FMP) set and F′ is a fractional strong matching preclusion (FSMP) set of G. The FMP (FSMP) number of G is the minimum size of FMP (FSMP) sets of G. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the Möbius cube MQn. In adddition, all the optimal fractional strong preclusion sets of these graphs are categorized.

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Chambers, Christopher P., and Federico Echenique. "The Core Matchings of Markets with Transfers." American Economic Journal: Microeconomics 7, no. 1 (2015): 144–64. http://dx.doi.org/10.1257/mic.20130089.

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We characterize the structure of the set of core matchings of an assignment game (a two-sided market with transfers). Such a set satisfies a property we call consistency. Consistency of a set of matchings states that, for any matching ν, if, for each agent i there exists a matching μ in the set for which μ there μ(i) = ν (i), then ν is in the set. A set of matchings satisfies consistency if and only if there is an assignment game for which all elements of the set maximize the surplus. (JEL C78)

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Han, Jie. "Perfect Matchings in Hypergraphs and the Erdös Matching Conjecture." SIAM Journal on Discrete Mathematics 30, no. 3 (2016): 1351–57. http://dx.doi.org/10.1137/16m1056079.

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Kotlar, Daniel, and Ran Ziv. "Large matchings in bipartite graphs have a rainbow matching." European Journal of Combinatorics 38 (May 2014): 97–101. http://dx.doi.org/10.1016/j.ejc.2013.11.011.

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Aliabadi, Mohsen, Majid Hadian, and Amir Jafari. "On matching property for groups and field extensions." Journal of Algebra and Its Applications 15, no. 01 (2015): 1650011. http://dx.doi.org/10.1142/s0219498816500110.

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In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions of division rings. We introduce the notion of relative matchings between arrays of elements in groups and use this notion to study the behavior of matchable sets under group homomorphisms. We also present infinite families of prime numbers p such that ℤ/pℤ does not have the acyclic matching property. Finally, we introduce the linear version of acyclic match

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Doslic, Tomislav, and Taylor Short. "Maximal matchings in polyspiro and benzenoid chains." Applicable Analysis and Discrete Mathematics 15, no. 1 (2021): 179–200. http://dx.doi.org/10.2298/aadm161106003d.

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A matching M of a graph G is maximal if it is not a proper subset of any other matching in G. Maximal matchings are much less known and researched than their maximum and perfect counterparts. In this paper we present the recurrences and generating functions for the sequences enumerating maximal matchings in two classes of chemically interesting linear polymers: polyspiro chains and benzenoid chains. We also analyze the asymptotic behavior of those sequences and determine the extremal cases.

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Movahedi, Fateme. "Matching polynomials for some nanostar dendrimers." Asian-European Journal of Mathematics 14, no. 10 (2021): 2150188. http://dx.doi.org/10.1142/s1793557121501886.

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Dendrimers are highly branched monodisperse, macromolecules and are considered in nanotechnology with a variety of suitable applications. In this paper, the matching polynomial and some results of the matchings for three classes of nanostar dendrimers are obtained. Furthermore, we express the recursive formulas of the Hosoya index for these structures of dendrimers by their matching polynomials.

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Antler, Yair. "Two-Sided Matching with Endogenous Preferences." American Economic Journal: Microeconomics 7, no. 3 (2015): 241–58. http://dx.doi.org/10.1257/mic.20130272.

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We modify the stable matching problem by allowing agents' preferences to depend on the endogenous actions of agents on the other side of the market. Conventional matching theory results break down in the modified setup. In particular, every game that is induced by a stable matching mechanism (e.g., the Gale-Shapley mechanism) may have equilibria that result in matchings that are not stable with respect to the agents' endogenous preferences. However, when the Gale-Shapley mechanism is slightly modified, every equilibrium of its induced game results in a pairwise stable matching with respect to

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KLAUS, BETTINA, and FLIP KLIJN. "EMPLOYMENT BY LOTTO REVISITED." International Game Theory Review 11, no. 02 (2009): 181–98. http://dx.doi.org/10.1142/s0219198909002248.

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We study employment by lotto (Aldershof et al., 1999), a procedurally fair matching algorithm for the so-called stable marriage problem. We complement Aldershof et al.'s (1999) analysis in two ways. First, we give an alternative and intuitive description of employment by lotto in terms of a probabilistic serial dictatorship on the set of stable matchings. Second, we show that Aldershof et al.'s (1999) conjectures are correct for small matching markets but not necessarily correct for large matching markets.

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