Clique covering of graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1986 English Publisher:Springer Science and Business Media LLCJournal:Combinatorica, volume 6, pages 393-398 (issn: 0209-9683, eissn: 1439-6912,

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Authors: László Pyber;

doi: 10.1007/bf02579265

Clique covering of graphs

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Abstract

The clique covering number cc(G) of a graph G is the least number of complete subgraphs of G necessary to cover the edge set of G. The author shows that there exists an integer \(n_ 0\) such that for all graphs G on \(n>n_ 0\) vertices \(\max \{cc(G)+cc(\bar G)\}=\lfloor n^ 2/4\rfloor +2.\) This settles a conjecture of Erdős.

Keywords

Extremal problems in graph theory, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), clique covering number

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