Improved bounds on linear coloring of plane graphs |
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Authors: | Wei Dong BaoGang Xu XiaoYan Zhang |
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Institution: | 1. School of Mathematical Science, Nanjing Normal University, Nanjing, 210097, China 2. School of Mathematics and Information Technology, Nanjing XiaoZhuang College, Nanjing, 210017, China
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Abstract: | A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we give some upper bounds on linear chromatic number for plane graphs with respect to their girth, that improve some results of Raspaud and Wang (2009). |
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