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

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

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

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

author: Louis Esperet, Mickaël Montassier and André Raspaud Linear choosability of graphs vertex-coloring, list, acyclic, 3-frugal, choosability under constraints. 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 3-colorable is an NP-complete problem. If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. 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 For a corresponding BibTeX entry, please consider our BibTeX-file. dmAE0120.ps.gz (64 K) dmAE0120.ps (174 K) dmAE0120.pdf (154 K)