2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 99-104

author: Louis Esperet, Mickaël Montassier and André Raspaud
title: Linear choosability of graphs
keywords: vertex-coloring, list, acyclic, 3-frugal, choosability under constraints.
abstract: A proper vertex coloring of a non oriented graph
is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph
-list colorable if for a given list assignment
L={L(v): v∈V}
, there exists a proper coloring
such that
for all
. If
-list colorable for every list assignment with
for all
, then
is said
-choosable. A graph is said to be lineary
-choosable if the coloring obtained is linear. In this paper, we investigate the linear choosability of graphs for some families of graphs: graphs with small maximum degree, with given maximum average degree, planar graphs... Moreover, we prove that determining whether a bipartite subcubic planar graph is lineary 3-colorable is an NP-complete problem.
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reference: Louis Esperet and Mickaël Montassier and André Raspaud (2005), Linear choosability of graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 99-104
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