Sparsity-parametrised dynamic edge colouring

We study the edge colouring problem on graphs of bounded arboricity, subject to insertions and deletions. We propose a max{deg(u), deg(v)} + O(α) edge colouring algorithm in poly(log n) time, with α the arboricity of the graph, which improves the state of the art for graphs of arboricity α = o(∆).