The mod k chromatic index of random graphs

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 1 (mod k). Recently, the authors proved that the mod k chromatic index of every graph is at most 198k - 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 C-k > 0 such that if p >= C-k n(-1) log n and n (1 - p) -> infinity as n -> infinity, then the following holds: if k is odd, then the mod k chromatic index of G (n, p) is asymptotically almost surely (a.a.s.) equal to k, while if k is even, then the mod k chromatic index of G(2n, p) (respectively, G(2n + 1, p)) is a.a.s. equal to k (respectively, k + 1).