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.
Published Version
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