The mod k $k$ chromatic index of random graphs

Abstract

The mod k chromatic index of a graph G is the minimum number of colors needed to color the edges of G in a way that the subgraph spanned by the edges of each color has all degrees congruent to k 1 (mod ).Recently, the authors proved that the mod k chromatic index of every graph is at most k 198 − 101, improving, for large k, a result of Scott.Here we study the mod k chromatic index of random graphs. We prove that for every integer  k 2, there, is the minimum number of colors in a χ′ k -coloring of G. Note that isolated vertices play no role in these definitions, and hence