On the Acyclic Chromatic Number of Hamming Graphs

Authors:
Robert E. Jamison;Gretchen L. Matthews
Affiliations:
(Affiliated Professor) University of Haifa, Mount Carmel, Israel and Clemson University, Department of Mathematical Sciences, 29634-0975, Clemson, SC, USA;Clemson University, Department of Mathematical Sciences, 29634-0975, Clemson, SC, USA
Venue:
Graphs and Combinatorics
Year:
2008

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Abstract

An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum number k such that G has an acyclic coloring with k colors. In this paper, acyclic colorings of Hamming graphs, products of complete graphs, are considered. Upper and lower bounds on the acyclic chromatic number of Hamming graphs are given.