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- W2126426226 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 prove that every planar graph G with girth g and maximum degree Δ has lc(G)=⌈Δ2⌉+1 if G satisfies one of the following four conditions: (1) g≥13 and Δ≥3; (2) g≥11 and Δ≥5; (3) g≥9 and Δ≥7; (4) g≥7 and Δ≥13. Moreover, we give better upper bounds of linear chromatic number for planar graphs with girth 5 or 6." @default.
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- W2126426226 date "2009-09-01" @default.
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- W2126426226 title "Linear coloring of planar graphs with large girth" @default.
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- W2126426226 doi "https://doi.org/10.1016/j.disc.2008.04.032" @default.
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