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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Linear choosability of graphs


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.
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hal-01184391 , version 1 (14-08-2015)



Louis Esperet, Mickael Montassier, André Raspaud. Linear choosability of graphs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.99-104, ⟨10.46298/dmtcs.3434⟩. ⟨hal-01184391⟩
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