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Journal articles on the topic 'Clique partition'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Shaohan, Ma, and W. D. Wallis. "Maximal-clique partitions of interval graphs." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 2 (1988): 227–32. http://dx.doi.org/10.1017/s1446788700030147.

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AbstractIt is shown that if an interval graph possesses a maximal-clique partition then its clique covering and clique partition numbers are equal, and equal to the maximal-clique partition number. Moreover an interval graph has such a partition if and only if all its maximal cliques are edge-disjoint.

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2

Jin, Cheng, Rong-Xia Hao, and Eddie Cheng. "The clique partition edge-fault numbers of some networks." Filomat 38, no. 22 (2024): 7923–33. https://doi.org/10.2298/fil2422923j.

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In a graph G, a clique partition of G is a partition P = {V1,V2, . . . ,Vq} of V(G) such that the induced subgraph G[Vi] is a clique (called a clique of P) for each i ? [q]. If a clique partition P also satisfies that |G[Vi]| = t for each i ? [q], the graph G is called a Kt-partitionable graph. A Kt-partition edge-fault set of G is a subset F of E(G) such that the deletion of F results in a graph where no Kt-partitions exist. The Kt-partition edge-fault number of G, denoted by ft(G), is the smallest size among all Kt-partition edge-fault sets of G. The Kt-preclusion number of G, denoted by 1t(

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3

Szabó, Sándor. "Metric space method for constructing splitting partitions of graphs." Acta Universitatis Sapientiae, Informatica 11, no. 2 (2019): 131–41. http://dx.doi.org/10.2478/ausi-2019-0009.

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Abstract In an earlier work [6] the concept of splitting partition of a graph was introduced in connection with the maximum clique problem. A splitting partition of a graph can be used to replace the graph by two smaller graphs in the course of a clique search algorithm. In other words splitting partitions can serve as a branching rule in an algorithm to compute the clique number of a given graph. In the paper we revisit this branching idea. We will describe a technique to construct not necessary optimal splitting partitions. The given graph can be viewed as a metric space and the geometry of

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DESSMARK, ANDERS, JESPER JANSSON, ANDRZEJ LINGAS, EVA-MARTA LUNDELL, and MIA PERSSON. "ON THE APPROXIMABILITY OF MAXIMUM AND MINIMUM EDGE CLIQUE PARTITION PROBLEMS." International Journal of Foundations of Computer Science 18, no. 02 (2007): 217–26. http://dx.doi.org/10.1142/s0129054107004656.

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We consider the following clustering problems: given an undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone classification. We investigate the hardness of finding such partitions and provide approximation algorithms. Further, we show that greedy strategies yield constant factor approximations for graph classes for which maximum cliques can be found efficiently.

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SIMANCHEV, R. Yu, and P. V. SOLOVIOVA. "bH-BASES FOR A SOME CLASS OF FACET OF A CLIQUE PARTITIONING POLYTOPE." Mathematical structures and modeling, no. 4 (2018): 27–33. http://dx.doi.org/10.24147/2222-8772.2018.4.27-33.

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Let Kn=(V,E) be a complete undirected \protect\lb n-vertex graph without loops and multiple edges. A spanning subgraph H⊂Kn is called an M-graph if each of its connected components (possibly single-vertex) is a clique. In other words, every M-graph is a regular partition of Kn into vertex-disjoint cliques. The family of all M-graphs in Kn is denoted by H. This family is the set of feasible solutions to the clique partition problem, which consists in finding an M-graph of minimum weight \cite{GroWak1990,GroWak1989,SU1} in a complete edge-weighted graph. The mentioned works consider the polyhedr

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Kang, Dong Yeap, and Sang-Il Oum. "Improper colouring of graphs with no odd clique minor." Combinatorics, Probability and Computing 28, no. 5 (2019): 740–54. http://dx.doi.org/10.1017/s0963548318000548.

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AbstractAs a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no oddKtminor is (t− 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for eacht⩾ 2, every graph with no oddKtminor has a partition of its vertex set into 6t− 9 setsV1, …,V6t−9such that eachViinduces a subgraph of bounded maximum degree. Secondly, we prove that for eacht⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 10t−13 setsV1,…,V10t−13such that eachViinduces a subgraph with components of bounded size. The second theorem

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7

Prisner, Erich. "Clique covering and clique partition in generalizations of line graphs." Discrete Applied Mathematics 56, no. 1 (1995): 93–98. http://dx.doi.org/10.1016/0166-218x(94)00076-p.

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8

Belyi, Alexander B., Stanislav L. Sobolevsky, Alexander N. Kurbatski, and Carlo Ratti. "Improved upper bounds in clique partitioning problem." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 29, 2019): 93–104. http://dx.doi.org/10.33581/2520-6508-2019-3-93-104.

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In this work, a problem of partitioning a complete weighted graph into cliques in such a way that sum of edge weights between vertices belonging to the same clique is maximal is considered. This problem is known as a clique partitioning problem. It arises in many applications and is a varian of classical clustering problem. However, since the problem, as well as many other combinatorial optimization problems, is NP-hard, finding its exact solution often appears hard. In this work, a new method for constructing upper bounds of partition quality function values is proposed, and it is shown how t

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9

Fu, Weiqi, Pan Shao, Ting Dong, and Zhewei Liu. "Novel Higher-Order Clique Conditional Random Field to Unsupervised Change Detection for Remote Sensing Images." Remote Sensing 14, no. 15 (2022): 3651. http://dx.doi.org/10.3390/rs14153651.

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Change detection (CD) is one of the most important topics in remote sensing. In this paper, we propose a novel higher-order clique conditional random field model to unsupervised CD for remote sensing images (termed HOC2RF), by defining a higher-order clique potential. The clique potential, constructed based on a well-designed higher-order clique of image objects, takes the interaction between the neighboring objects in both feature and location spaces into account. HOC2RF consists of five principle steps: (1) Two difference images with complementary change information are produced by change ve

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10

Erdős, Paul, Edward T. Ordman, and Yechezkel Zalcstein. "Clique Partitions of Chordal Graphs." Combinatorics, Probability and Computing 2, no. 4 (1993): 409–15. http://dx.doi.org/10.1017/s0963548300000808.

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To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.

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11

Jones, Átila A., Fábio Protti та Renata R. Del-Vecchio. "Edge clique partition in (k,ℓ)-graphs". Discrete Applied Mathematics 306 (січень 2022): 89–97. http://dx.doi.org/10.1016/j.dam.2021.09.035.

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12

Dumitrescu, Adrian, and János Pach. "Minimum Clique Partition in Unit Disk Graphs." Graphs and Combinatorics 27, no. 3 (2011): 399–411. http://dx.doi.org/10.1007/s00373-011-1026-1.

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13

Li, Chu-Min, and Zhe Quan. "An Efficient Branch-and-Bound Algorithm Based on MaxSAT for the Maximum Clique Problem." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (2010): 128–33. http://dx.doi.org/10.1609/aaai.v24i1.7536.

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State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partition P. In this way, the strength of specific algorithms for Maxclique in partitioning a graph and the strength of MaxSAT technology in propositional reasoning are naturally combined to solve Maxclique. E

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14

Palubeckis, Gintaras, Armantas Ostreika, and Arūnas Tomkevičius. "An Iterated Tabu Search Approach for the Clique Partitioning Problem." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/353101.

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Given an edge-weighted undirected graph with weights specifying dissimilarities between pairs of objects, represented by the vertices of the graph, the clique partitioning problem (CPP) is to partition the vertex set of the graph into mutually disjoint subsets such that the sum of the edge weights over all cliques induced by the subsets is as small as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. The proposed algorithm incorporates tabu search, local search, and solution perturbation procedures. We report computational results on CPP instances of size u

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Chen, Baiyu, Junwen Ding, Canhui Luo, Qingyun Zhang, Zhouxing Su, and Zhipeng Lü. "An Elite-guided Weighted Simulated Annealing Algorithm for the Clique Partitioning Problem." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 25 (2025): 26904–12. https://doi.org/10.1609/aaai.v39i25.34895.

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The clique partitioning problem (CPP) aims to find a partition of vertices of a complete graph in order to maximize the sum of edge weights within each partition (clique), which has been proven to be NP-hard and has wide real-world applications. In this paper, we propose an elite-guided weighted simulated annealing algorithm called EWSA to solve the CPP. First, EWSA employs two specific configurations and alternates between them via an oscillation strategy, which balances the exploitation and exploration of the search. Second, a weighting strategy is introduced to improve the scoring function

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16

Hudry, Olivier. "Application of the “descent with mutations” metaheuristic to a clique partitioning problem." RAIRO - Operations Research 53, no. 3 (2019): 1083–95. http://dx.doi.org/10.1051/ro/2018048.

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We study here the application of the “descent with mutations” metaheuristic to a problem arising from the field of classification and cluster analysis (dealing more precisely with the aggregation of symmetric relations) and which can be represented as a clique partitioning of a weighted graph. In this problem, we deai with a complete undirected graphe G; the edges of G have weights which can be positive, negative or equal to 0; the aim is to partition the vertices of G into disjoint cliques (whose number depends on G in order to minimize the sum of the weights of the edges with their two extre

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17

FUNABIKI, NOBUO, YOSHIYASU TAKEFUJI, KUO CHUN LEE, and YONG BEOM CHO. "A neural network parallel algorithm for clique vertex-partition problems." International Journal of Electronics 72, no. 3 (1992): 357–72. http://dx.doi.org/10.1080/00207219208925578.

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18

Bärmann, Andreas, Patrick Gemander, Alexander Martin, and Maximilian Merkert. "On Recognizing Staircase Compatibility." Journal of Optimization Theory and Applications 195, no. 2 (2022): 449–79. http://dx.doi.org/10.1007/s10957-022-02091-2.

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AbstractFor the problem to find an m-clique in an m-partite graph, staircase compatibility has recently been introduced as a polynomial-time solvable special case. It is a property of a graph together with an m-partition of the vertex set and total orders on each subset of the partition. In optimization problems involving m-cliques in m-partite graphs as a subproblem, it allows for totally unimodular linear programming formulations, which have shown to efficiently solve problems from different applications. In this work, we address questions concerning the recognizability of this property in t

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19

LIAO, Zhuo-Fan, Jian-Xin WANG, and Shi-Geng ZHANG. "Relay Placement Algorithms Based on Clique Partition in WiMAX Mesh Networks." Chinese Journal of Computers 36, no. 5 (2014): 937–46. http://dx.doi.org/10.3724/sp.j.1016.2013.00937.

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20

HU, Gang, Ming XU, Li-Xia LIU, Hong-Jian LI, and Yu-Xing PENG. "Spectrum Sensing Algorithm Based on Clique Partition for Wireless Cognitive Networks." Journal of Software 22, no. 2 (2011): 298–312. http://dx.doi.org/10.3724/sp.j.1001.2011.03721.

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21

Penev, Irena. "Perfect Graphs with No Balanced Skew-Partition are 2-Clique-Colorable." Journal of Graph Theory 81, no. 3 (2015): 213–35. http://dx.doi.org/10.1002/jgt.21870.

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22

Al-Addasi, Salah. "The Complementary Join of a Graph." WSEAS TRANSACTIONS ON MATHEMATICS 23 (March 8, 2024): 147–53. http://dx.doi.org/10.37394/23206.2024.23.17.

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The complementary join of a graph G is introduced in this paper as the join G+G of G and its complement considering them as vertex-disjoint graphs. The aim of this paper is to study some properties and some graph invariants of the complementary join of a graph. We find the diameter, the radius and the domination number of G + G and determine when G + G is self-centered. We obtain a characterization of the Eulerian complementary joins, and show that the complementary join of a nontrivial graph is Hamiltonian. We give the clique and independence numbers of G + G in terms of the clique and indepe

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23

VU, VAN. "A Simple SVD Algorithm for Finding Hidden Partitions." Combinatorics, Probability and Computing 27, no. 1 (2017): 124–40. http://dx.doi.org/10.1017/s0963548317000463.

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Finding a hidden partition in a random environment is a general and important problem which contains as subproblems many important questions, such as finding a hidden clique, finding a hidden colouring, finding a hidden bipartition, etc.In this paper we provide a simple SVD algorithm for this purpose, addressing a question of McSherry. This algorithm is easy to implement and works for sparse graphs under optimal density assumptions. We also consider an approximating algorithm, which on one hand works under very mild assumptions, but on other hand can sometimes be upgraded to give the exact sol

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Chen, Mingxia, Jianbo Li, Jianping Li, Weidong Li, and Lusheng Wang. "Some approximation algorithms for the clique partition problem in weighted interval graphs." Theoretical Computer Science 381, no. 1-3 (2007): 124–33. http://dx.doi.org/10.1016/j.tcs.2007.04.030.

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Pirwani, Imran A., and Mohammad R. Salavatipour. "A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs." Algorithmica 62, no. 3-4 (2011): 1050–72. http://dx.doi.org/10.1007/s00453-011-9503-8.

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26

Glaria, Felipe, Cecilia Hernández, Susana Ladra, Gonzalo Navarro, and Lilian Salinas. "Compact structure for sparse undirected graphs based on a clique graph partition." Information Sciences 544 (January 2021): 485–99. http://dx.doi.org/10.1016/j.ins.2020.09.010.

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27

Baransky, Vitaly, Valentin Zuev, and Tatiana Senchonok. "REDUCING GRAPHS BY LIFTING ROTATIONS OF EDGES TO SPLITTABLE GRAPHS." Ural Mathematical Journal 10, no. 2 (2024): 25. https://doi.org/10.15826/umj.2024.2.003.

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A graph \(G\) is splittable if its set of vertices can be represented as the union of a clique and a coclique. We will call a graph \(H\) a splittable ancestor of a graph \(G\) if the graph \(G\) is reducible to the graph \(H\) using some sequential lifting rotations of edges and \(H\) is a splittable graph. A splittable \(r\)-ancestor of \(G\) we will call its splittable ancestor whose Durfey rank is \(r\). Let us set \(s = ({1}/{2}) (\mathrm{sum}\,\mathrm{tl}(\lambda) - \mathrm{sum}\,\mathrm{hd}(\lambda))\), where \(\mathrm{hd}(\lambda)\) and \(\mathrm{tl}(\lambda)\) are the head and the tai

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Faruqi, Shahab, S. A. Katre, and Manisha Garg. "Pseudo orthogonal Latin squares." Discrete Mathematics and Applications 31, no. 1 (2021): 5–17. http://dx.doi.org/10.1515/dma-2021-0002.

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Abstract Two Latin squares A, B of order n are called pseudo orthogonal if for any 1 ≤ i, j ≤ n there exists a k, 1 ≤ k ≤ n, such that A(i, k) = B(j, k). We prove that the existence of a family of m mutually pseudo orthogonal Latin squares of order n is equivalent to the existence of a family of m mutually orthogonal Latin squares of order n. We also obtain exact values of clique partition numbers of several classes of complete multipartite graphs and of the tensor product of complete graphs.

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Satti, Mansoor. "Families of Disjoint Sets Colouring Technique and Concept of Common Face and Non-Common Face." International Journal for Scientific Research 4, no. 1 (2025): 323–45. https://doi.org/10.59992/ijsr.2025.v4n1p12.

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Families of disjoint sets colouring technique is trial to generalize all type of colouring and partition. This paper related to face colouring, in this paper we introduce the concept of common face and non-common face, and used two methods to determine adjacency of faces. We introduce some results related to the concept of common face and results related to non-common face, and introduce some results explain the number of minimum colour classes not changed after addition or after removal of non-common face, if maximum clique number is constant.

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Weron, Tomasz, and Janusz Szwabiński. "Opinion Evolution in Divided Community." Entropy 24, no. 2 (2022): 185. http://dx.doi.org/10.3390/e24020185.

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Our agent-based model of opinion dynamics concerns the current vast divisions in modern societies. It examines the process of social polarization, understood here as the partition of a community into two opposing groups with contradictory opinions. Our goal is to measure how mutual animosities between parties may lead to their radicalization. We apply a double-clique topology with both positive and negative ties to the model of binary opinions. Individuals are subject to social pressure; they conform to the opinions of their own clique (positive links) and oppose those from the other one (nega

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Long, Xiangyu, Shufan Wu, Xiaofeng Wu, Yixin Huang, and Zhongcheng Mu. "A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions." Algorithms 12, no. 11 (2019): 231. http://dx.doi.org/10.3390/a12110231.

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This paper presents a space mission planning tool, which was developed for LEO (Low Earth Orbit) observation satellites. The tool is focused on a two-phase planning strategy with clustering preprocessing and mission planning, where an improved clustering algorithm is applied, and a hybrid algorithm that combines the genetic algorithm with the simulated annealing algorithm (GA–SA) is given and discussed. Experimental simulation studies demonstrate that the GA–SA algorithm with the improved clique partition algorithm based on the graph theory model exhibits higher fitness value and better optimi

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32

Mullins, Derrick, and Matthew Hayes. "The minimum weight clique partition problem and its application to structural variant calling." International Journal of Computational Biology and Drug Design 13, no. 5/6 (2020): 475. http://dx.doi.org/10.1504/ijcbdd.2020.10036394.

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Hayes, Matthew, and Derrick Mullins. "The minimum weight clique partition problem and its application to structural variant calling." International Journal of Computational Biology and Drug Design 13, no. 5/6 (2020): 475. http://dx.doi.org/10.1504/ijcbdd.2020.113829.

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ASANO, TAKAO. "DYNAMIC PROGRAMMING ON INTERVALS." International Journal of Computational Geometry & Applications 03, no. 03 (1993): 323–30. http://dx.doi.org/10.1142/s0218195993000208.

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We consider problems on intervals which can be solved by dynamic programming. Specifically, we give an efficient implementation of dynamic programming on intervals. As an application, an optimal sequential partition of a graph G=(V, E) can be obtained in O(m log n) time, where n=|V| and m=|E|. We also present an O(n log n) time algorithm for finding a minimum weight dominating set of an interval graph G=(V, E), and an O(m log n) time algorithm for finding a maximum weight clique of a circular-arc graph G=(V, E), provided their intersection models of n intervals (arcs) are given.

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Kurnia, Rian, Ahmad Muchlas Abrar, Abdul Gazir Syarifudin, Verrel Rievaldo Wijaya, Nur Ain Supu, and Erma Suwastika. "ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 3 (2023): 1463–72. http://dx.doi.org/10.30598/barekengvol17iss3pp1463-1472.

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The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices s

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Busygin, Stanislav, and Dmitrii V. Pasechnik. "On NP-hardness of the clique partition—Independence number gap recognition and related problems." Discrete Mathematics 306, no. 4 (2006): 460–63. http://dx.doi.org/10.1016/j.disc.2006.01.004.

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ALI, HESHAM H., and HESHAM EL-REWINI. "ON THE INTRACTABILITY OF TASK ALLOCATION IN DISTRIBUTED SYSTEMS." Parallel Processing Letters 04, no. 01n02 (1994): 149–57. http://dx.doi.org/10.1142/s0129626494000168.

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The fast progress of large integration technology has made distributed computing economically attractive for many computer applications. Task allocation is one of the most important and challenging problems in distributed computing systems that has received considerable attention in recent years. Several researchers have introduced different heuristics to solve this problem with the assumption that it is computationally intractable. These researchers have been referring to an early work by Stone and some private communication as their sources of the problem’s intractability. However, neither S

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Huang, Yixin, Zhongcheng Mu, Shufan Wu, Benjie Cui, and Yuxiao Duan. "Revising the Observation Satellite Scheduling Problem Based on Deep Reinforcement Learning." Remote Sensing 13, no. 12 (2021): 2377. http://dx.doi.org/10.3390/rs13122377.

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Earth observation satellite task scheduling research plays a key role in space-based remote sensing services. An effective task scheduling strategy can maximize the utilization of satellite resources and obtain larger objective observation profits. In this paper, inspired by the success of deep reinforcement learning in optimization domains, the deep deterministic policy gradient algorithm is adopted to solve a time-continuous satellite task scheduling problem. Moreover, an improved graph-based minimum clique partition algorithm is proposed for preprocessing in the task clustering phase by con

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O'Neil, Thomas E. "Complement, Complexity, and Symmetric Representation." International Journal of Foundations of Computer Science 26, no. 05 (2015): 557–81. http://dx.doi.org/10.1142/s0129054115500318.

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A representation for a set is defined to be symmetric if the space required for the representation of the set is the same as the space required for representation of the set's complement. The use of symmetric representation is shown to be important when studying the time complexity of algorithms. A symmetric data structure called a flip list is defined, and it is employed for the Clique, Independent Set, and Vertex Cover problems in a case study. The classic reductions among these problems require the complement of either a graph's edge set or a subset of its vertices. Flip lists can be comple

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Cerioli, M. R., L. Faria, T. O. Ferreira, and F. Protti. "On minimum clique partition and maximum independent set on unit disk graphs and penny graphs: complexity and approximation." Electronic Notes in Discrete Mathematics 18 (December 2004): 73–79. http://dx.doi.org/10.1016/j.endm.2004.06.012.

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KOTEK, TOMER. "Complexity of Ising Polynomials." Combinatorics, Probability and Computing 21, no. 5 (2012): 743–72. http://dx.doi.org/10.1017/s0963548312000259.

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This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and external field. One may consider such an Ising system as a simple graph together with vertex and edge weights. When these weights are considered indeterminates, the partition function for the constant case is a trivariate polynomialZ(G;x,y,z). This polynomial was studied with respect to its approximability by Goldberg, Jerrum and Paterson.Z(G;x,y,z) generalizes a

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Qi, Xingqin, Ruth Luo, Edgar Fuller, Rong Luo, and Cun-Quan Zhang. "Signed Quasi-Clique Merger: A New Clustering Method for Signed Networks with Positive and Negative Edges." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 03 (2016): 1650006. http://dx.doi.org/10.1142/s0218001416500063.

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Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlap

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Lai, Wei-Yu, and Tien-Ruey Hsiang. "Wireless Charging Deployment in Sensor Networks." Sensors 19, no. 1 (2019): 201. http://dx.doi.org/10.3390/s19010201.

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Charging schemes utilizing mobile wireless chargers can be applied to prolong the lifespan of a wireless sensor network. In considering charging schemes with mobile chargers, most current studies focus on charging each sensor from a single position, then optimizing the moving paths of the chargers. However, in reality, a wireless charger may charge the same sensor from several positions in its path. In this paper we consider this fact and seek to minimize both the number of charging locations and the total required charging time. Two charging plans are developed. The first plan considers the c

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Eslahchi, Ch, and A. M. Rahimi. "Thek-Zero-Divisor Hypergraph of a Commutative Ring." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–15. http://dx.doi.org/10.1155/2007/50875.

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The concept of the zero-divisor graph of a commutative ring has been studied by many authors, and thek-zero-divisor hypergraph of a commutative ring is a nice abstraction of this concept. Though some of the proofs in this paper are long and detailed, any reader familiar with zero-divisors will be able to read through the exposition and find many of the results quite interesting. LetRbe a commutative ring andkan integer strictly larger than2. Ak-uniform hypergraphHk(R)with the vertex setZ(R,k), the set of allk-zero-divisors inR, is associated toR, where eachk-subset ofZ(R,k)that satisfies thek-

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Konar, Aritra, and Nicholas D. Sidiropoulos. "Optimal Quasi-clique: Hardness, Equivalence with Densest-k-Subgraph, and Quasi-partitioned Community Mining." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 8608–16. http://dx.doi.org/10.1609/aaai.v38i8.28705.

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Dense subgraph discovery (DSD) is a key primitive in graph mining that typically deals with extracting cliques and near-cliques. In this paper, we revisit the optimal quasi-clique (OQC) formulation for DSD and establish that it is NP--hard. In addition, we reveal the hitherto unknown property that OQC can be used to explore the entire spectrum of densest subgraphs of all distinct sizes by appropriately varying a single hyperparameter, thereby forging an intimate link with the classic densest-k-subgraph problem (DkS). We corroborate these findings on real-world graphs by applying the simple gre

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Muthammai, S., and R. Mahalakshmi. "Clique Partition Numbers of Boolean Function Graphs B(K_P, L(G), INC, NINC) and B(K_P, L(G), INC, NINC)." International Journal of Engineering Science, Advanced Computing and Bio-Technology 8, no. 3 (2017): 156. http://dx.doi.org/10.26674/ijesacbt/2017/49183.

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Erdöos, Paul, Ralph Faudree, and Edward T. Ordman. "Clique partitions and clique coverings." Discrete Mathematics 72, no. 1-3 (1988): 93–101. http://dx.doi.org/10.1016/0012-365x(88)90197-5.

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Pandurangan, Gopal, Peter Robinson, and Michele Scquizzato. "On the Distributed Complexity of Large-Scale Graph Computations." ACM Transactions on Parallel Computing 8, no. 2 (2021): 1–28. http://dx.doi.org/10.1145/3460900.

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Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n >> k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main contribution is the G

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Erskine, Grahame, Terry Griggs, and Jozef Širáň. "Clique-partitioned graphs." Discrete Applied Mathematics 314 (June 2022): 238–48. http://dx.doi.org/10.1016/j.dam.2022.02.024.

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Cavers, Michael S., Randall J. Elzinga, David A. Gregory, Sarah E. Vanderlinde, and Kevin N. Vander Meulen. "Clique partitions of distance multigraphs." Discrete Mathematics 308, no. 15 (2008): 3230–40. http://dx.doi.org/10.1016/j.disc.2007.06.028.

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