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 3-colorable is an NP-complete problem.
Highlights
Linear choosability of graphsTo cite this version: 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. hal-01184391
A proper vertex coloring of a graph is linear if the graph induced by the vertices of two color classes is a forest of paths
Theorem 6 Deciding whether a bipartite subcubic planar graph is lineary 3-colorable is an NP-complete problem
Summary
To cite this version: 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. hal-01184391. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. 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 , G is said k-choosable. A graph is said to be lineary k-choosable if the coloring obtained is linear.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have