A (k, r)-hued coloring of a graph G is a proper k-coloring phi such that vertical bar phi(N-G(v))vertical bar >= min{d(G)(v), r} for any vertex v. The r-hued chromatic number of G, written chi r (G), is the minimum integer k such that G has a (k, r)-hued coloring. In this paper, we show that chi r (G) <= r + 5 if r >= 13 and G is a planar graph without 3,4,8-cycles or if G is a planar graph without 4,5-cycles and no 3-cycle is intersect with i-cycles, i = {3, 6, 7}, then chi r (G) <= r + 5, where r >= 3.
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机译：图G的（k，r）曲线图G是适当的K-着色PHI，使得垂直条PHI（NG（V））垂直条> = MIN {D（G）（V），R}对于任何顶点 v。G，写入CHI R（G）的R-SUED色谱数是最小整数k，使得G具有（k，r）-hued着色。 在本文中，我们表明Chi R（g）<= r + 5如果r> = 13和g是没有3,4,8-循环的平面图，或者如果g是平面图，则没有4,5-循环 没有3周期与I-循环相交，i = {3,6,7}，然后是Chi R（g）<= r + 5，其中r> = 3。
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