Document Type

Article

Department/Program

Physics

Journal Title

European Journal of Combinatorics

Pub Date

2013

Volume

34

Issue

6

First Page

1040

Abstract

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induces 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,K-3. This confirms a conjecture raised by Esperet, Montassier and Raspaud [L Esperet, M. Montassier, and A. Raspaud, Linear choosability of graphs, Discrete Math. 308 (2008) 3938-3950]. Our proof is constructive and yields a linear-time algorithm to find such a coloring. (C) 2013 Elsevier Ltd. All rights reserved.

DOI

10.1016/j.ejc.2013.02.008

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