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Machado, Raphael C.S.; de Figueiredo, Celina M.H.; Trotignon, Nicolas
Discrete mathematics, 07/2013, Volume: 313, Issue: 14Journal Article
A graph G is 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≥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.
