On the conjunctive capacity of graphs

M. Chlebik, Janka Chlebikova

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

The investigation of the asymptotic behaviour of various graph parameters in powers of a fixed graph G=(V,E) is motivated by problems in information theory and extremal combinatorics. Considering various parameters and/or various notions of graph powers we can arrive at different notions of graph capacities, of which the Shannon capacity is best known. Here we study a related notion of the so-called conjunctive capacity of a graph G, C_AND(G), introduced and studied by Gargano, K\"orner and Vaccaro. To determine C_AND(G) is a convex programming problem. In this paper we show that the optimal solution to this problem is unique and describe the structure of the solution in any (simple) graph. We show that its reciprocal value vc_C(G):=1/C_AND(G is an optimal solution of the newly introduced problem of Minimum Capacitary Vertex Cover that is closely related to the LP-relaxation of the Minimum Vertex Cover Problem. We also describe its close connection with the binding number/binding set of a graph, and with the strong crown decomposition of graphs.
Original languageEnglish
Title of host publicationComputing and combinatorics: 19th International Conference, COCOON 2013, Hangzhou, China, June 21-23, 2013, proceedings
EditorsD-Z. Du, G. Zhang
Place of PublicationBerlin
PublisherSpringer
Pages280-291
Number of pages12
Volume7936
Edition7936
ISBN (Print)9783642387678
DOIs
Publication statusPublished - 2013

Publication series

NameLecture notes in computer science
PublisherSpringer-Verlag
Number7936

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