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arXiv · 1506.05719

A Coloring Algorithm for $4K_1$-free line graphs

Dallas J. Fraser·Angèle M. Hamel·Chính T. Hoàng
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Abstract

Let $L$ be a set of graphs. $Free$($L$) is the set of graphs that do not contain any graph in $L$ as an induced subgraph. It is known that if $L$ is a set of four-vertex graphs, then the complexity of the coloring problem for $Free$($L$) is known with three exceptions: $L $= {claw, $4K_1$}, $L$ = {claw, $4K_1$, co-diamond}, and $L$ = {$C_4$, $4K_1$}. In this paper, we study the coloring problem for $Free$(claw, $4K_1$). We solve the coloring problem for a subclass of $Free$(claw, $4K_1$) which contains the class of $4K_1$-free line graphs. Our result implies the chromatic index of a graph with no matching of size four can be computed in polynomial time.

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BibTeXRIS

Dallas J. Fraser, Angèle M. Hamel, Chính T. Hoàng. 2015-06-18. A Coloring Algorithm for $4K_1$-free line graphs. https://arxiv.org/abs/1506.05719

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