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Free choosability of outerplanar graphs. (English) Zbl 1339.05065
Summary: 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 $$u\neq v$$, 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.
##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C15 Coloring of graphs and hypergraphs 05C38 Paths and cycles
##### Keywords:
coloring; choosability; free choosability; cycle; outerplanar graph
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##### References:
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