1. Acyclic edge coloring of subcubic graphs
- Author
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Basavaraju, Manu and Sunil Chandran, L.
- Subjects
- *
GRAPH coloring , *MATHEMATICAL analysis , *GRAPHIC methods , *GRAPH theory , *MATHEMATICS - Abstract
Abstract: An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number such that there is an acyclic edge coloring using colors and it is denoted by . From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors. [Copyright &y& Elsevier]
- Published
- 2008
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