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Journal articles on the topic 'Large graphs'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

PERARNAU, G., та B. REED. "Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree". Combinatorics, Probability and Computing 26, № 3 (2016): 448–67. http://dx.doi.org/10.1017/s0963548316000328.

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Let ℱ be a family of graphs and letdbe large enough. For everyd-regular graphG, we study the existence of a spanning ℱ-free subgraph ofGwith large minimum degree. This problem is well understood if ℱ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we study a locally injective analogue of the question.

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2

FÜRER, MARTIN, and SHIVA PRASAD KASIVISWANATHAN. "Approximately Counting Embeddings into Random Graphs." Combinatorics, Probability and Computing 23, no. 6 (2014): 1028–56. http://dx.doi.org/10.1017/s0963548314000339.

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LetHbe a graph, and letCH(G) be the number of (subgraph isomorphic) copies ofHcontained in a graphG. We investigate the fundamental problem of estimatingCH(G). Previous results cover only a few specific instances of this general problem, for example the case whenHhas degree at most one (the monomer-dimer problem). In this paper we present the first general subcase of the subgraph isomorphism counting problem, which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labelling of the vertices such that every edge

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3

Ábrego, Bernardo M., Ruy Fabila-Monroy, Silvia Fernández-Merchant, et al. "Proximity graphs inside large weighted graphs." Networks 61, no. 1 (2012): 29–39. http://dx.doi.org/10.1002/net.21464.

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4

Lovász, László. "Very Large Graphs." Current Developments in Mathematics 2008, no. 1 (2008): 67–128. http://dx.doi.org/10.4310/cdm.2008.v2008.n1.a2.

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5

Hu, Yifan, and Lei Shi. "Visualizing large graphs." Wiley Interdisciplinary Reviews: Computational Statistics 7, no. 2 (2015): 115–36. http://dx.doi.org/10.1002/wics.1343.

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6

Shao, Zehui, Jin Xu, S. M. Sheikholeslami, and Shaohui Wang. "The Domination Complexity and Related Extremal Values of Large 3D Torus." Complexity 2018 (July 2, 2018): 1–8. http://dx.doi.org/10.1155/2018/3041426.

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Domination is a structural complexity of chemical molecular graphs. A dominating set in a (molecular) graphG=V,Eis a subsetS⊆Vsuch that each vertex inV\Sis adjacent to at least one vertex inS. The domination numberγGof a graphGis the minimum size of a dominating set inG. In this paper, computer-aided approaches for obtaining bounds for domination number on torus graphs are here considered, and many new exact values and bounds are obtained.

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7

Cheng, Hong, Yang Zhou, and Jeffrey Xu Yu. "Clustering Large Attributed Graphs." ACM Transactions on Knowledge Discovery from Data 5, no. 2 (2011): 1–33. http://dx.doi.org/10.1145/1921632.1921638.

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8

Kollios, G., M. Potamias, and E. Terzi. "Clustering Large Probabilistic Graphs." IEEE Transactions on Knowledge and Data Engineering 25, no. 2 (2013): 325–36. http://dx.doi.org/10.1109/tkde.2011.243.

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9

Bollobás, Béla, and Vladimir Nikiforov. "Large joints in graphs." European Journal of Combinatorics 32, no. 1 (2011): 33–44. http://dx.doi.org/10.1016/j.ejc.2010.07.010.

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10

Hudák, Peter, Mária Maceková, Tomas Madaras, and Pavol Široczki. "Light graphs in planar graphs of large girth." Discussiones Mathematicae Graph Theory 36, no. 1 (2016): 227. http://dx.doi.org/10.7151/dmgt.1847.

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11

Shafir, Ofer. "Universal graphs without large bipartite graphs assuming GCH." Discrete Mathematics 256, no. 1-2 (2002): 509–12. http://dx.doi.org/10.1016/s0012-365x(01)00229-1.

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12

Guldan, Filip. "Note on linear arboricity of graphs with large girth." Czechoslovak Mathematical Journal 41, no. 3 (1991): 467–70. http://dx.doi.org/10.21136/cmj.1991.102481.

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13

Hoang, Dô Trong, Nguyên Công Minh, and Trân Nam Trung. "Cohen–Macaulay graphs with large girth." Journal of Algebra and Its Applications 14, no. 07 (2015): 1550112. http://dx.doi.org/10.1142/s0219498815501121.

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14

Wichianpaisarn, Tanawat, and Chariya Uiyyasathian. "Graphs with large clique-chromatic numbers." Discrete Mathematics, Algorithms and Applications 07, no. 04 (2015): 1550055. http://dx.doi.org/10.1142/s179383091550055x.

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The clique-chromatic number of a graph [Formula: see text], [Formula: see text], is the least number of colors on [Formula: see text] without a monocolored maximal clique of size at least two. If [Formula: see text] is triangle-free, [Formula: see text]; we then consider only graphs with a triangle. Unlike the chromatic number, the clique-chromatic number of a graph is not necessary to be at least those of its subgraphs. Thus, for any family of graphs [Formula: see text], the boundedness of [Formula: see text][Formula: see text] has been investigated. Many families of graphs are proved to have

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15

Bray, John, Christopher Parker, and Peter Rowley. "Cayley type graphs and cubic graphs of large girth." Discrete Mathematics 214, no. 1-3 (2000): 113–21. http://dx.doi.org/10.1016/s0012-365x(99)00222-8.

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16

Hajduk, Róbert, and Roman Soták. "On large light graphs in families of polyhedral graphs." Discrete Mathematics 310, no. 3 (2010): 417–22. http://dx.doi.org/10.1016/j.disc.2009.03.008.

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17

Collins, Karen L., and Megan E. Heenehan. "Constructing Graphs with No Immersion of Large Complete Graphs." Journal of Graph Theory 77, no. 1 (2013): 1–18. http://dx.doi.org/10.1002/jgt.21770.

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18

Yuster, Raphael. "Decomposing large graphs with small graphs of high density." Journal of Graph Theory 32, no. 1 (1999): 27–40. http://dx.doi.org/10.1002/(sici)1097-0118(199909)32:1<27::aid-jgt3>3.0.co;2-c.

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19

John, J., and M. S. Malchijah Raj. "Graphs with large Steiner number." Ukrains’kyi Matematychnyi Zhurnal 76, no. 5 (2024): 719–27. http://dx.doi.org/10.3842/umzh.v76i5.7409.

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UDC 519.1 In 2002, Gary Chartrand and Ping Zhang [<em>The Steiner number of a graph,</em> Discrete Math., <strong>242</strong>, 41--54 (2002)] characterized the connected graphs G of order p ≥ 3 with Steiner number p , p - 1 , or 2. In our paper, we characterize all connected graphs G of order p ≥ 4 with Steiner number s ( G ) = p - 2 . In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected.

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20

YUSTER, RAPHAEL. "Dense Graphs With a Large Triangle Cover Have a Large Triangle Packing." Combinatorics, Probability and Computing 21, no. 6 (2012): 952–62. http://dx.doi.org/10.1017/s0963548312000235.

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It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-free, in the sense that it is necessary to remove roughly m/2 edges in order to eliminate all triangles.We prove that dense graphs that are hard to make triangle-free have a large packing of pairwise edge-disjoint triangles. In particular, they have more than m(1/4+cβ) pairwise edge-disjoint triangles where β is the density of the graph and c ≥ is an absolute constant. This improves upon a previous m

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21

Mattiolo, D., G. Mazzuoccolo, and G. Tabarelli. "Graphs with large palette index." Discrete Mathematics 345, no. 5 (2022): 112814. http://dx.doi.org/10.1016/j.disc.2022.112814.

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22

Yousuf, Muhammad Irfan, and Suhyun Kim. "List sampling for large graphs." Intelligent Data Analysis 22, no. 2 (2018): 261–95. http://dx.doi.org/10.3233/ida-163319.

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23

BIGGS, N. L. "Cubic Graphs with Large Girth." Annals of the New York Academy of Sciences 555, no. 1 Combinatorial (1989): 56–62. http://dx.doi.org/10.1111/j.1749-6632.1989.tb22437.x.

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24

Ahangar Abdollahzadeh, Hossein, Saeed Kosari, Seyed Sheikholeslami, and Lutz Volkmann. "Graphs with large geodetic number." Filomat 29, no. 6 (2015): 1361–68. http://dx.doi.org/10.2298/fil1506361a.

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25

Adamaszek, Anna, and MichaŁ Adamaszek. "Large-Girth Roots of Graphs." SIAM Journal on Discrete Mathematics 24, no. 4 (2010): 1501–14. http://dx.doi.org/10.1137/100792949.

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26

Andriantiana, Eric Ould Dadah, and Stephan Wagner. "Unicyclic graphs with large energy." Linear Algebra and its Applications 435, no. 6 (2011): 1399–414. http://dx.doi.org/10.1016/j.laa.2011.03.013.

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27

Soffer, Sara Nadiv. "Graphs with many large degrees." Discrete Mathematics 239, no. 1-3 (2001): 171–77. http://dx.doi.org/10.1016/s0012-365x(01)00049-8.

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28

Alon, Noga, Eldar Fischer, Michael Krivelevich, and Mario Szegedy. "Efficient Testing of Large Graphs." Combinatorica 20, no. 4 (2000): 451–76. http://dx.doi.org/10.1007/s004930070001.

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29

Fang, Meng, Jie Yin, and Xingquan Zhu. "Active exploration for large graphs." Data Mining and Knowledge Discovery 30, no. 3 (2015): 511–49. http://dx.doi.org/10.1007/s10618-015-0424-z.

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30

Yousuf, Muhammad Irfan, and Suhyun Kim. "Guided sampling for large graphs." Data Mining and Knowledge Discovery 34, no. 4 (2020): 905–48. http://dx.doi.org/10.1007/s10618-020-00683-y.

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31

Gómez, J., M. A. Fiol та O. Serra. "On large (Δ,D)-graphs". Discrete Mathematics 114, № 1-3 (1993): 219–35. http://dx.doi.org/10.1016/0012-365x(93)90368-4.

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32

Džamonja, M., J. A. Larson, and W. J. Mitchell. "Partitions of large Rado graphs." Archive for Mathematical Logic 48, no. 6 (2009): 579–606. http://dx.doi.org/10.1007/s00153-009-0138-2.

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33

Ding, Guoli, and Peter Chen. "Unavoidable doubly connected large graphs." Discrete Mathematics 280, no. 1-3 (2004): 1–12. http://dx.doi.org/10.1016/j.disc.2003.05.006.

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34

Wexler, Mark. "Matrix models on large graphs." Nuclear Physics B 410, no. 2 (1993): 377–94. http://dx.doi.org/10.1016/0550-3213(93)90439-v.

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35

Alon, Noga, Dan Hefetz, Michael Krivelevich, and Mykhaylo Tyomkyn. "Edge-statistics on large graphs." Combinatorics, Probability and Computing 29, no. 2 (2019): 163–89. http://dx.doi.org/10.1017/s0963548319000294.

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AbstractThe inducibility of a graph H measures the maximum number of induced copies of H a large graph G can have. Generalizing this notion, we study how many induced subgraphs of fixed order k and size ℓ a large graph G on n vertices can have. Clearly, this number is $\left( {\matrix{n \cr k}}\right)$ for every n, k and $\ell \in \left\{ {0,\left( {\matrix{k \cr 2}} \right)}\right\}$. We conjecture that for every n, k and $0 \lt \ell \lt \left( {\matrix{k \cr 2}}\right)$ this number is at most $ (1/e + {o_k}(1)) {\left( {\matrix{n \cr k}} \right)}$. If true, this would be tight for ℓ ∈ {1, k

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36

Kajdanowicz, Tomasz, Przemyslaw Kazienko, and Wojciech Indyk. "Parallel processing of large graphs." Future Generation Computer Systems 32 (March 2014): 324–37. http://dx.doi.org/10.1016/j.future.2013.08.007.

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37

Canale, Eduardo A., та José Gómez. "Asymptotically large (Δ,D)-graphs". Discrete Applied Mathematics 152, № 1-3 (2005): 89–108. http://dx.doi.org/10.1016/j.dam.2005.03.008.

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38

Halperin, Alexander, Colton Magnant, and Hua Wang. "On large semi-linked graphs." Discrete Mathematics 338, no. 1 (2015): 122–29. http://dx.doi.org/10.1016/j.disc.2014.08.022.

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39

Chen, Jing, and Genghua Fan. "Large even factors of graphs." Journal of Combinatorial Optimization 35, no. 1 (2017): 162–69. http://dx.doi.org/10.1007/s10878-017-0161-x.

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40

Shi, Lingsheng, and Hongyu Xu. "Large Induced Forests in Graphs." Journal of Graph Theory 85, no. 4 (2016): 759–79. http://dx.doi.org/10.1002/jgt.22104.

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41

Alon, Noga. "Testing subgraphs in large graphs." Random Structures and Algorithms 21, no. 3-4 (2002): 359–70. http://dx.doi.org/10.1002/rsa.10056.

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42

Bordenave, Charles, and Marc Lelarge. "Resolvent of large random graphs." Random Structures & Algorithms 37, no. 3 (2010): 332–52. http://dx.doi.org/10.1002/rsa.20313.

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43

Koutra, Danai, U. Kang, Jilles Vreeken, and Christos Faloutsos. "Summarizing and understanding large graphs." Statistical Analysis and Data Mining: The ASA Data Science Journal 8, no. 3 (2015): 183–202. http://dx.doi.org/10.1002/sam.11267.

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44

Martí, J. Gómez. "On large (Δ, 6)-Graphs". Networks 46, № 2 (2005): 82–87. http://dx.doi.org/10.1002/net.20075.

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45

Komjath, P., and S. Shelah. "Universal Graphs without Large Cliques." Journal of Combinatorial Theory, Series B 63, no. 1 (1995): 125–35. http://dx.doi.org/10.1006/jctb.1995.1008.

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46

Delorme, C., and J. Gómez. "Some New Large Compound Graphs." European Journal of Combinatorics 23, no. 5 (2002): 539–47. http://dx.doi.org/10.1006/eujc.2002.0581.

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47

Vengerovsky, V. "Eigenvalue Distribution of Bipartite Large Weighted Random Graphs. Resolvent Approach." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 1 (2016): 78–93. http://dx.doi.org/10.15407/mag12.01.078.

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48

Huo, Qingyi, and Long-Tu Yuan. "Graphs with large maximum degree containing no edge-critical graphs." European Journal of Combinatorics 106 (December 2022): 103576. http://dx.doi.org/10.1016/j.ejc.2022.103576.

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49

Lagraa, Sofiane, Hamida Seba, Riadh Khennoufa, Abir M׳Baya, and Hamamache Kheddouci. "A distance measure for large graphs based on prime graphs." Pattern Recognition 47, no. 9 (2014): 2993–3005. http://dx.doi.org/10.1016/j.patcog.2014.03.014.

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50

Chou, Chung-Hsien, Phillip Sheu, Masahiro Hayakawa, and Atsushi Kitazawa. "Querying large graphs in biomedicine with colored graphs and decomposition." Journal of Biomedical Informatics 108 (August 2020): 103503. http://dx.doi.org/10.1016/j.jbi.2020.103503.

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