Edge-colouring and total-colouring chordless graphs

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 $\mathrm{\Delta }\ge 3$ has chromatic index $\mathrm{\Delta }$ and total chromatic number $\Delta

• 1$. The proofs are algorithmic in the sense that we actually output an optimal colouring of a graph instance in polynomial time.