The Power of Multi-Step Vizing Chains

We prove new properties of multi-step Vizing chains, which lead to improved algorithms for:
* distributed (Δ+1) edge-colouring in the LOCAL model, and
* worst-case dynamic (1+ ε) Δ edge-colouring in the randomised adaptive model
As a consequence of these new insights, the "local Vizing theorem" follows, i.e. that every edge can be coloured with a colour between 0 and the largest degree of an endpoint.