Edge-colouring and total-colouring chordless graphs

Raphael C.S. Machado, Celina M.H. de Figueiredo, Nicolas Trotignon
2013 Discrete Mathematics  
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.
doi:10.1016/j.disc.2013.03.020 fatcat:oye6jvujxzg7zc6pjn7h65gfii