Relevant bibliographies by topics / Clique partition

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Clique partition'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Clique partition"

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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Clique partition"

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Phan, Raksmey. "Méthodes exactes et approchées par partition en cliques de graphes." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00921589.

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Cette thèse se déroule au sein du projet ToDo (Time versus Optimality in discrete Optimization ANR 09-EMER-010) financé par l'Agence Nationale de la Recherche. Nous nous intéressons à la résolution exacte et approchée de deux problèmes de graphes. Dans un souci de compromis entre la durée d'exécution et la qualité des solutions, nous proposons une nouvelle approche par partition en cliques qui a pour but (1) de résoudre de manière rapide des problèmes exacts et (2) de garantir la qualité des résultats trouvés par des algorithmes d'approximation. Nous avons combiné notre approche avec des techn
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Wellens, Jake(Jake Lee). "Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126937.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020<br>Cataloged from the official PDF of thesis.<br>Includes bibliographical references (pages 107-112).<br>This thesis consists of three disparate parts. In the first, we generalize and extend recent ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant variables for a boolean function in terms of its degree, its sensitivity, and its certificate and decision tree complexities, and we also sharpen the best-known polynomial relationships between some of these complexity measures
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Martin, Jean-Noel. "No Free Lunch et recherche de solutions structurantes en coloration." Phd thesis, Université de Technologie de Belfort-Montbeliard, 2010. http://tel.archives-ouvertes.fr/tel-00607481.

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Nous présentons d'abord les théorèmes du No Free Lunch en nous basant sur le papier de D.H. Wolpert et W.G. Macready (version IEEE 1997) mais aussi les multiples réactions que ces résultats ont provoquées dans la communauté de l'optimisation. Convaincus dès lors de l'intérêt d'une approche globale des problèmes et de la nécessité de la recherche de propriétés générales - et spécialement des invariances par symétries -, nous tentons ensuite de mettre en oeuvre cette méthode dans le cadre de la coloration de graphes simples et non orientés. Ce champ est retenu en raison de son intérêt propre, ma
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Guo, Jun-Lin, and 郭俊麟. "On Edge Clique Partitions and set Representations of Graphs." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/88591848218469752612.

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碩士<br>東海大學<br>數學系<br>97<br>In 1966 Erd¨os et al. [8] proved that the edge set of any simple graph G with n vertices, no one of which is isolated vertex, can be partitioned using at most ⌊n2/4⌋ cliques. A couple of tens of years behind McGuinness proved that any greedy clique partition is such a partition. In this paper we prove that any set representation corresponding to it wouldn't use more than ⌊n2/4⌋ element.
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Book chapters on the topic "Clique partition"

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Eidenbenz, Stephan, and Christoph Stamm. "Maximum Clique and Minimum Clique Partition in Visibility Graphs." In Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44929-9_16.

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Belyi, Alexander, and Stanislav Sobolevsky. "Network Size Reduction Preserving Optimal Modularity and Clique Partition." In Computational Science and Its Applications – ICCSA 2022. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10522-7_2.

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Li, Jianbo, Mingxia Chen, Jianping Li, and Weidong Li. "Minimum Clique Partition Problem with Constrained Weight for Interval Graphs." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11809678_48.

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Wang, Jiahai, Xinshun Xu, Zheng Tang, Weixing Bi, Xiaoming Chen, and Yong Li. "A New Neural Network Algorithm for Clique Vertex-Partition Problem." In Advances in Neural Networks – ISNN 2004. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-28647-9_71.

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Fleischer, Rudolf, and Xiaotian Wu. "Edge Clique Partition of K 4-Free and Planar Graphs." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24983-9_9.

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Pirwani, Imran A., and Mohammad R. Salavatipour. "A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13731-0_19.

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Pardalos, Panos M., and Steffen Rebennack. "Computational Challenges with Cliques, Quasi-cliques and Clique Partitions in Graphs." In Experimental Algorithms. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13193-6_2.

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Bryś, Krzysztof, and Zbigniew Lonc. "Clique and anticlique partitions of graphs." In Graph-Theoretic Concepts in Computer Science. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-62559-3_7.

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Wallis, W. D. "The Clique Partition Number of the Complement of a Cycle." In Annals of Discrete Mathematics (27): Cycles in Graphs. Elsevier, 1985. http://dx.doi.org/10.1016/s0304-0208(08)73026-3.

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Wu Guang-Ting, Sheu Ruey-Kai, Fan Chih-Tien, Chang Yue-Shan, and Tai Chih-Hua. "Adaptive Block Partition of Geographic Map Based on Road Coverage in Urban Environment." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2015. https://doi.org/10.3233/978-1-61499-484-8-1416.

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Smart cities try to deploy new sensors or controller to existing hardware infrastructure to improve the efficiency of city life. How to effectively utilize geographic information to deploy ubiquitous facilities (such as street light control unit) in the urban environment increasingly becomes an important issue. Calculating the minimum block number for facility deployment in a city is similar to the maximum clique problem which belongs to the NP-hard problems. In this paper, we propose an algorithm to find the near minimum block number of geographic map based on road coverage in the urban envir
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Conference papers on the topic "Clique partition"

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Liu, Pei-qiang. "Research on Greedy Clique Partition-GCP Algorithm." In 2006 International Conference on Machine Learning and Cybernetics. IEEE, 2006. http://dx.doi.org/10.1109/icmlc.2006.259018.

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Zhuofan Liao, Jianxin Wang, Shigeng Zhang, and Jiannong Cao. "Clique partition based relay placement in WiMAX mesh networks." In GLOBECOM 2012 - 2012 IEEE Global Communications Conference. IEEE, 2012. http://dx.doi.org/10.1109/glocom.2012.6503503.

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Zhang, Yan-ping, Xiao-yan Chen, Bo Hua, and Yuan Zhang. "A Maximal Clique Partition Method for Network Based on Granularity." In 2011 Seventh International Conference on Computational Intelligence and Security (CIS). IEEE, 2011. http://dx.doi.org/10.1109/cis.2011.99.

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Long, Jun, Shilong Chen, Cong Li, and Junfeng Liu. "A Task Clustering Method for Multi Agile Satellite Based on Clique Partition." In 2018 11th International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2018. http://dx.doi.org/10.1109/icicta.2018.00082.

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Long, Xiangyu, Shufan Wu, Benjie Cui, Zhongcheng Mu, Yixin Huang, and Sunhao Chu. "Analysis of satellite observation task clustering based on the improved clique partition algorithm." In 2019 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2019. http://dx.doi.org/10.1109/cec.2019.8790243.

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Monteiro, Bruno, and Vinicius Dos Santos. "Equitable Partition of Graphs into Independent Sets and Cliques." In IV Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/etc.2019.6392.

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A graph is (k, l) if its vertex set can be partitioned into k independent sets and l cliques. Deciding if a graph is (k, l) can be seen as a generalization of coloring, since deciding is a graph belongs to (k, 0) corresponds to deciding if a graph is k-colorable. A coloring is equitable if the cardinalities of the color classes differ by at most 1. In this paper, we generalize both the (k, l) and the equitable coloring problems, by showing that deciding whether a given graph can be equitably partitioned into k independent sets and l cliques is solvable in polynomial time if max(k, l) 2, and NP
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Feder, Tomás, and Rajeev Motwani. "Clique partitions, graph compression and speeding-up algorithms." In the twenty-third annual ACM symposium. ACM Press, 1991. http://dx.doi.org/10.1145/103418.103424.

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Horauer, Martin, Harald Schuster, and Peter Balog. "Experimental Assessment of the Clique Problem in FlexRay." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12888.

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The FlexRay bus protocol recently adopted by the automotive industry provides both a time- and event-triggered communication paradigm, combined with communication via two independent channels, as well as optional bus-guardians in order to meet the bandwidth and reliability requirements by present and future emerging automotive applications. Despite the benefits and improvements, when compared to traditional bus systems (e.g., CAN), rare faults may still occur. In this regard, this paper presents an experimental investigation of the clique problem, where a FlexRay network gets partitioned into
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