Choosability, introduced by Erdős, Rubin, and Taylor [Congr. Number. 1979], is a well-studied concept in graph theory: we say that a graph is c-choosable if for any assignment of a list of c colors to each vertex, there is a proper coloring where each vertex uses a color from its list. We study the complexity of deciding choosability on graphs of bounded treewidth. It follows from earlier work ...

Let S(r) denote a circle of circumference r. The circular consecutive choosability chcc(G) of a graph G is the least real number t such that for any r > χc(G), if each vertex v is assigned a closed interval L(v) of length t on S(r), then there is a circular r-colouring f of G such that f(v) ∈ L(v). We investigate, for a graph, the relations between its circular consecutive choosability and choo...

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) → 2, there exists a 2-frugal (resp. linear) colouring c of G such that c(v) ∈ L(v) for all v ∈ V (G). If G is 2-frugally...