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- W2334754952 abstract "For a graph $G$, let $cn(G)$ and $la(G)$ denote the chromatic number of $G$ and the maximum local edge connectivity of $G$, respectively. A result of Dirac cite{Dirac53} implies that every graph $G$ satisfies $cn(G)leq la(G)+1$. In this paper we characterize the graphs $G$ for which $cn(G)=la(G)+1$. The case $la(G)=3$ was already solved by Alboulker {em et al.,} cite{AlboukerV2016}. We show that a graph $G$ with $la(G)=kgeq 4$ satisfies $cn(G)=k+1$ if and only if $G$ contains a block which can be obtained from copies of $K_{k+1}$ by repeated applications of the Hajos join." @default.
- W2334754952 created "2016-06-24" @default.
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- W2334754952 date "2016-03-30" @default.
- W2334754952 modified "2023-10-01" @default.
- W2334754952 title "A Brooks type theorem for the maximum local edge connectivity" @default.
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