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 ∆(G) + 2 is the bound for the acyclic edge chromatic number of any graph G. It also represents an analogue of a result of Robinson and the second author on edge chromatic number. Partially supported by the Project LN00A056 of the Czech Ministery of Education and performed in part while visiting CRM, Bellatera, Spain. Research supported in part by the Australian Research Council and performed in part while visiting CRM, Bellatera, Spain.