Dyck's map (3, 7)8 is a counterexample to a clique covering conjecture

A. Vince; Steve Wilson

doi:10.1016/0095-8956(92)90074-8

Dyck's map (3, 7)₈ is a counterexample to a clique covering conjecture

A. Vince, Steve Wilson

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let c(G) denote the minimum number of cliques necessary to cover all edges of a graph G. A counterexample is provided to a conjecture communicated by P. Erdo{combining double acute accent}s. If c(G - e) < c(G) for every edge e, then G contains no triangles.

Original language	English (US)
Pages (from-to)	157-160
Number of pages	4
Journal	Journal of Combinatorial Theory, Series B
Volume	54
Issue number	1
DOIs	https://doi.org/10.1016/0095-8956(92)90074-8
State	Published - Jan 1992

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(92)90074-8

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title = "Dyck's map (3, 7)8 is a counterexample to a clique covering conjecture",

abstract = "Let c(G) denote the minimum number of cliques necessary to cover all edges of a graph G. A counterexample is provided to a conjecture communicated by P. Erdo\{combining double acute accent\}s. If c(G - e) < c(G) for every edge e, then G contains no triangles.",

author = "A. Vince and Steve Wilson",

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AB - Let c(G) denote the minimum number of cliques necessary to cover all edges of a graph G. A counterexample is provided to a conjecture communicated by P. Erdo{combining double acute accent}s. If c(G - e) < c(G) for every edge e, then G contains no triangles.

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Dyck's map (3, 7)₈ is a counterexample to a clique covering conjecture

Abstract

ASJC Scopus subject areas

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