A note on the acyclic 3-choosability of some planar graphs
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چکیده
منابع مشابه
A note on the acyclic 3-choosability of some planar graphs
An acyclic coloring of a graph G is a coloring of its vertices such that : (i) no two adjacent vertices in G receive the same color and (ii) no bicolored cycles exist in G. A list assignment of G is a function L that assigns to each vertex v ∈ V (G) a list L(v) of available colors. Let G be a graph and L be a list assignment of G. The graph G is acyclically L-list colorable if there exists an a...
متن کاملA note on the not 3-choosability of some families of planar graphs
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 any list assignment with |L(v)| k for all v ∈ V , then G is said k-choosable. In [M. Voigt, A not 3-choosable planar graph without 3-cycles, Discrete Math. 146 (1995) 325–328] and [M. Voigt, A non-3choosable plan...
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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...
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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 کاملA note on 3-choosability of planar graphs without certain cycles
Steinberg asked whether every planar graph without 4 and 5 cycles is 3-colorable. Borodin, and independently Sanders and Zhao, showed that every planar graph without any cycle of length between 4 and 9 is 3-colorable. We improve this result by showing that every planar graph without any cycle of length 4, 5, 6, or 9 is 3-choosable. © 2005 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2010
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.02.005