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arXiv · 1309.1842

Edge-colouring and total-colouring chordless graphs

Raphael C. S. Machado·Celina M. H. de Figueiredo·Nicolas Trotignon
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Abstract

A graph $G$ is \emph{chordless} if no cycle in $G$ has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree $Δ\geq 3$ has chromatic index $Δ$ and total chromatic number $Δ+ 1$. The proofs are algorithmic in the sense that we actually output an optimal colouring of a graph instance in polynomial time.

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Raphael C. S. Machado, Celina M. H. de Figueiredo, Nicolas Trotignon. 2013-09-07. Edge-colouring and total-colouring chordless graphs. https://doi.org/10.1016/j.disc.2013.03.020

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