Edge-colouring and total-colouring chordless graphs

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.