- 著者
-
Asahi Takaoka
Shingo Okuma
Satoshi Tayu
Shuichi Ueno
- 雑誌
- 研究報告アルゴリズム(AL)
- 巻号頁・発行日
- vol.2014, no.11, pp.1-6, 2014-11-13
The harmonious coloring of a 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 of determining 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 known as caterpillars. This paper shows the harmonious chromatic number of shooting stars and comets, which are ones of the simplest kinds of caterpillar. We also show the upper bound of harmonious chromatic number of 3-regular caterpillars.The harmonious coloring of a 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 of determining 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 known as caterpillars. This paper shows the harmonious chromatic number of shooting stars and comets, which are ones of the simplest kinds of caterpillar. We also show the upper bound of harmonious chromatic number of 3-regular caterpillars.