Mathematics > Combinatorics
[Submitted on 23 Jun 2012 (v1), last revised 23 Feb 2013 (this version, v2)]
Title:Linear colorings of subcubic graphs
View PDFAbstract:A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and every assignment of lists of size four to the vertices of the graph, there exists a linear coloring such that the color of each vertex belongs to the list assigned to that vertex and the neighbors of every degree-two vertex receive different colors, unless the graph is $C_5$ or $K_{3,3}$. This confirms a conjecture raised by Esperet, Montassier, and Raspaud. Our proof is constructive and yields a linear-time algorithm to find such a coloring.
Submission history
From: Chun-Hung Liu [view email][v1] Sat, 23 Jun 2012 01:31:28 UTC (12 KB)
[v2] Sat, 23 Feb 2013 21:24:13 UTC (14 KB)
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