Vizing's and Shannon's Theorems for defective edge colouring

Pierre Aboulker, Guillaume Aubian, Chien-Chung Huang

We call a multigraph $(k,d)$-edge colourable if its edge set can be partitioned into $k$ subgraphs of maximum degree at most $d$ and denote as ${\chi }_d^{\prime }(G)$ the minimum $k$ such that…