The acyclic edge chromatic number of a random d‐regular graph is d+ 1

We prove the theorem from the title: the acyclic edge chromatic number of a random d‐regular graph is asymptotically almost surely equal to d+ 1. This improves a result of Alon, Sudakov, and Zaks and presents further support for a conjecture that Δ(G) + 2 is the bound for the acyclic edge chromatic number of any graph G. It also represents an analog of a result of Robinson and the second author on edge chromatic number. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 69–74, 2005