Local version of Vizing's theorem for multi-graphs

Clinton T. Conley, Jan Grebik, Oleg Pikhurko

Extending a result of Christiansen, we prove that every mutli-graph $G=(V,E)$ admits a proper edge colouring $\varphi :E\to \{1,2,\dots \}$ which is local, that is, $ϕ(e)\le \max\{d(x)+π(x…