The mod k $k$ chromatic index of random graphs

Abstract The mod chromatic index of a graph is the minimum number of colors needed to color the edges of in a way that the subgraph spanned by the edges of each color has all degrees congruent to . Recently, the authors proved that the mod chromatic index of every graph is at most , improving, for large , a result of Scott. Here we study the mod chromatic index of random graphs. We prove that for every integer , there is such that if and as , then the following holds: if is odd, then the mod chromatic index of is asymptotically almost surely (a.a.s.) equal to , while if is even, then the mod chromatic index of (respectively, ) is a.a.s. equal to (respectively, ).