Acyclic edge coloring of subcubic graphs |
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Authors: | Manu Basavaraju |
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Institution: | Computer Science and Automation Department, Indian Institute of Science, Bangalore-560012, India |
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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 k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). 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. |
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Keywords: | Acyclic edge coloring Acyclic edge chromatic index Subcubic graphs |
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