2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 99104
author:  Louis Esperet, Mickaël Montassier and André Raspaud 

title:  Linear choosability of graphs 
keywords:  vertexcoloring, list, acyclic, 3frugal, choosability under constraints. 
abstract: 
A proper vertex coloring of a non oriented graph
G=(V,E)
is linear if the graph induced by the
vertices of two color classes is a forest of paths. A graph
G
is
L
list colorable if for a given list assignment
L={L(v): v∈V}
, there exists a proper coloring
c
of
G
such that
c(v)∈L(v)
for all
v∈V
. If
G
is
L
list colorable for every list assignment with
L(v)≥k
for all
v∈V
, then
G
is said
k
choosable. A graph is said to be lineary
k
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 3colorable is
an NPcomplete 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. 99104 
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