【摘 要】
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For positive integers k and r, an (k, r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree i will be adjacent to ver
【机 构】
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DepartmentofMathematics,RenminUniversityofChina,Beijing100872,China.
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For positive integers k and r, an (k, r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree i will be adjacent to vertices with at least min{i, r} different colors.The smallest integer k for which a graph has an (k, r)-coloring is the r-hued chromatic number xr (G).It is known that there exist families of graphs in which the difference between xr(G) and the classic chromatic number tends to infinity.It has been one of the main research stream problems to identify graph families in which In this the difference between xr (G) and the classic chromatic number is bounded.We investigate the 3-hued chromatic number of claw-free graphs and give out its best possible upper bound.
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