Extending partial edge colorings

Pál Bärnkopf, Ervin Győri

Published 2023-10-15Version 1

We consider the problem of extending partial edge colorings of (iterated) cartesian products of even cycles and paths, focusing on the case when the precolored edges constitute a matching. We prove the conjecture of Casselgren, Granholm and Petros that a precolored distance 3 matching in the Cartesian product of two even cycles can be extended to a 4-coloring of the edge set of the whole graph. Actually, a generalization for the Cartesian product of two bipartite graphs is proved.