The 3-choosability of plane graphs of girth 4
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چکیده
منابع مشابه
The 3-choosability of plane graphs of girth 4
A set S of vertices of the graph G is called k-reducible if the following is true: G is k-choosable if and only if G − S is k-choosable. A k-reduced subgraph H of G is a subgraph of G such that H contains no k-reducible set of some specific forms. In this paper, we show that a 3-reduced subgraph of a non-3-choosable plane graph G contains either adjacent 5-faces, or an adjacent 4-face and kface...
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Thomassen proved that any plane graph of girth 5 is list-colorable from any list assignment such that all vertices have lists of size two or three and the vertices with list of size two are all incident with the outer face and form an independent set. We present a strengthening of this result, relaxing the constraint on the vertices with list of size two. This result is used to bound the size o...
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A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)| = k for every edge and face x , there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree ∆(G) is (∆(G)+ 3)-edge-face choosable. © 2004 Elsevier ...
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متن کامل3-choosability of Planar Graphs with ( 4)-cycles Far Apart
A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.10.023