Acyclic colorings of subcubic graphs

Authors:
San Skulrattanakulchai
Affiliations:
Department of Mathematics and Computer Science, Gustavus Adolphus College, St. Peter, MN
Venue:
Information Processing Letters
Year:
2004

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Abstract

It is known that the acyclic chromatic number of a subcubic graph is at most four, and its acyclic edge chromatic number is at most five. We present algorithms that prove these two facts. Let n be the number of vertices of a graph, Our first algorithm takes O(n) time and uses four colors to properly color the vertices of any subcubic graph so that there is no 2-colored cycle. Our second algorithm takes O(n) time and uses five colors to properly color the edges of any subcubic graph so that there is no 2-colored cycle. Both are the first linear-time algorithms for the problems they solve.