Article ID Journal Published Year Pages File Type
4649499 Discrete Mathematics 2010 6 Pages PDF
Abstract

A graph GG is (k+1)(k+1)-critical if it is not kk-colourable but G−eG−e is kk-colourable for any edge e∈E(G)e∈E(G). In this paper we show that for any integers k≥3k≥3 and l≥5l≥5 there exists a constant c=c(k,l)>0c=c(k,l)>0, such that for all ñ, there exists a (k+1)(k+1)-critical graph GG on nn vertices with n>ñ and odd girth at least ℓℓ, which can be made (k−1)(k−1)-colourable only by the omission of at least cn2cn2 edges.

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Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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