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Pré-Publication, Document De Travail Année : 2010

Extended core and choosability of a graph

Résumé

A graph $G$ is $(a,b)$-choosable if for any color list of size $a$ associated with each vertices, one can choose a subset of $b$ colors such that adjacent vertices are colored with disjoint color sets. This paper shows an equivalence between the $(a,b)$-choosability of a graph and the $(a,b)$-choosability of one of its subgraphs called the extended core. As an application, this result allows to prove the $(5,2)$-choosability and $(7,3)$-colorability of triangle-free induced subgraphs of the triangular lattice.
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Dates et versions

hal-00492157 , version 1 (15-06-2010)

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Yves Aubry, Godin Jean-Christophe, Togni Olivier. Extended core and choosability of a graph. 2010. ⟨hal-00492157⟩
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