Linear Colouring of Planar Graphs with Prescribed Girth and Maximum Degree
نویسندگان
چکیده
A linear colouring of a graph is a proper vertex colouring such that the subgraph induced by any two colour classes is a set of vertex disjoint paths. The corresponding linear chromatic number of a graph G, namely lc(G), is the minimum number of colours in a linear colouring of G. We prove that for a graph G with girth g ≥ 8 and maximum degree ∆ ≥ 7 the inequality on its linear colouring number holds: lc(G) ≤ ⌈∆2 ⌉+1. This improves the girth assumption of a previously known bound of Raspaud and Wang [9].
منابع مشابه
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تاریخ انتشار 2011