The 2-dipath chromatic number of Halin graphs |
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Authors: | Chen Min |
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Affiliation: | Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China |
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Abstract: | A 2-dipath k-coloring f of an oriented graph is a mapping from to the color set {1,2,…,k} such that f(x)≠f(y) whenever two vertices x and y are linked by a directed path of length 1 or 2. The 2-dipath chromatic number of is the smallest k such that has a 2-dipath k-coloring. In this paper we prove that if is an oriented Halin graph, then . There exist infinitely many oriented Halin graphs such that . |
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Keywords: | Combinatorial problems Oriented coloring Halin graph |
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