IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
A Note on Harmonious Coloring of Caterpillars
Asahi TAKAOKAShingo OKUMASatoshi TAYUShuichi UENO
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2015 Volume E98.D Issue 12 Pages 2199-2206

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Abstract

The harmonious coloring of an undirected simple graph is a vertex coloring such that adjacent vertices are assigned different colors and each pair of colors appears together on at most one edge. The harmonious chromatic number of a graph is the least number of colors used in such a coloring. The harmonious chromatic number of a path is known, whereas the problem to find the harmonious chromatic number is NP-hard even for trees with pathwidth at most 2. Hence, we consider the harmonious coloring of trees with pathwidth 1, which are also known as caterpillars. This paper shows the harmonious chromatic number of a caterpillar with at most one vertex of degree more than 2. We also show the upper bound of the harmonious chromatic number of a 3-regular caterpillar.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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