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Linear and 2-Frugal Choosability of Graphs of Small Maximum Average Degree

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Abstract

A proper vertex colouring of a graph G is 2-frugal (resp. linear) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). A graph G is 2-frugally (resp. linearly) L-colourable if for a given list assignment \({L:V(G)\mapsto 2^{\mathbb N}}\) , there exists a 2-frugal (resp. linear) colouring c of G such that \({c(v) \in L(v)}\) for all \({v\in V(G)}\) . If G is 2-frugally (resp. linearly) L-list colourable for any list assignment such that |L(v)| ≥ k for all \({v\in V(G)}\), then G is 2-frugally (resp. linearly) k-choosable. In this paper, we improve some bounds on the 2-frugal choosability and linear choosability of graphs with small maximum average degree.

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Authors and Affiliations

  1. Projet Mascotte, CNRS/INRIA/UNSA, INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902, Sophia-Antipolis Cedex, France

    Nathann Cohen & Frédéric Havet

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  1. Nathann Cohen
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  2. Frédéric Havet
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Correspondence to Nathann Cohen.

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Partially supported by the ANR Blanc International Taiwan GRATEL.

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Cohen, N., Havet, F. Linear and 2-Frugal Choosability of Graphs of Small Maximum Average Degree. Graphs and Combinatorics 27, 831–849 (2011). https://doi.org/10.1007/s00373-010-1009-7

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  • DOI: https://doi.org/10.1007/s00373-010-1009-7

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