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

Authors:
Jaroslav Nešetřil;Nicholas C. Wormald
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské Nám. 25, 11800 Praha 1, Czech Republic;Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON N2L 3G1, Canada
Venue:
Journal of Graph Theory
Year:
2005

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Abstract

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 AMS classification: 05C15 (primary: graph coloring) 68R05 (secondary: combinatorics).