【摘 要】
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For positive integers k and r, a (k, r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to verti
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For positive integers k and r, a (k, r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d, r} different colors.The r-hued chromatic number, denoted by xr(G), is the smallest integer k for which a graph G has a (k, r)-coloring.In this paper, some results on upper bounds for r-hued chromatic number of planar graphs are given.
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