Acyclic 4-choosability of planar graphs
نویسندگان
چکیده
منابع مشابه
Acyclic 4-choosability of planar graphs
A proper vertex coloring of a graph G = (V , E) is acyclic if G contains no bicolored cycle. Given a list assignment L = {L(v) | v ∈ V } of G, we say G is acyclically L-list colorable if there exists a proper acyclic coloring π of G such that π(v) ∈ L(v) for all v ∈ V . If G is acyclically L-list colorable for any list assignment with |L(v)| ≥ k for all v ∈ V , then G is acyclically k-choosable...
متن کاملAcyclic improper choosability of graphs
We consider improper colorings (sometimes called generalized, defective or relaxed colorings) in which every color class has a bounded degree. We propose a natural extension of improper colorings: acyclic improper choosability. We prove that subcubic graphs are acyclically (3,1)∗-choosable (i.e. they are acyclically 3-choosable with color classes of maximum degree one). Using a linear time algo...
متن کاملOn the acyclic choosability of graphs
A proper vertex coloring of a graph G = (V, E) is acyclic if G contains no bicolored cycle. A graph G is L-list colorable if for a given list assignment L = {L(v) : v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is L-list colorable for every list assignment with |L(v)| ≥ k for all v ∈ V , then G is said k-choosable. A graph is said to be acyclically k-...
متن کامل(4, 2)-Choosability of Planar Graphs with Forbidden Structures
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any l∈{3,4,5,6,7}" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; ...
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: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.10.003