Abstract
A 2 -dipath k-coloring f of an oriented graph G → is a mapping from V ( G → ) 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 χ → 2 ( G → ) of G → is the smallest k such that G → has a 2-dipath k-coloring. In this paper we prove that if G → is an oriented Halin graph, then χ → 2 ( G → ) ⩽ 7 . There exist infinitely many oriented Halin graphs G → such that χ → 2 ( G → ) = 7 .
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