Free Choosability of Outerplanar Graphs.

A graph G is free ( a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex $$u\ne v$$ , the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free ( a, b)-choosable is given. As a corollary, we obtain almost optimal results about the free ( a, b)-choosability of outerplanar graphs. [ABSTRACT FROM AUTHOR]