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New Upper Bounds on Linear Coloring of Planar Graphs
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New Upper Bounds on Linear Coloring of Planar Graphs
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Journal Article
New Upper Bounds on Linear Coloring of Planar Graphs
2012
Overview
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, it is proved that every planar graph G with girth g and maximum degree A has （1） lc（G） ≤ △ ＋ 21 if △ ≥ 9; （2） lc（G） ≤[△/2]＋ 7 if g≥5; （3） lc（G） ≤ [△/2]＋2ifg≥7and△ ≥7.
