Free Choosability of Outerplanar Graphs
نویسندگان
چکیده
منابع مشابه
Free Choosability of Outerplanar Graphs
AgraphG 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 = 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 corollar...
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It is proved that, if G is a K4-minor-free graph with maximum degree ∆ > 4, then G is totally (∆ + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ∆ + 1 colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours. Together with other known results, t...
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A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k ≥ 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2015
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-015-1625-3