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A note on the acyclic 3choosability of some planar graphs
, 2009
"... 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 a ..."
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and L be a list assignment of G. The graph G is acyclically Llist colorable if there exists an acyclic coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V (G). If G is acyclically Llist colorable for any list assignment L with L(v)  ≥ k for all v ∈ V (G), then G is acyclically kchoosable
Some structural properties of planar graphs and their applications to 3choosability
, 2009
"... In this article, we consider planar graphs in which each vertex is not incident to some cycles of given lengths, but all vertices can have different restrictions. This generalizes the approach based on forbidden cycles which corresponds to the case where all vertices have the same restrictions on th ..."
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on the incident cycles. We prove that a planar graph G is 3choosable if it is satisfied one of the following conditions: (1) each vertex x is neither incident to cycles of lengths 4,9, ix with ix ∈ {5, 7,8}, nor incident to 6cycles adjacent to a 3cycle. (2) each vertex x is not incident to cycles of lengths 4
Every planar graph without cycles of length 4 to 12 is acyclically 3choosable. LaBRI Research Report RR146209
, 2009
"... 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 a ..."
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Cited by 1 (1 self)
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and L be a list assignment of G. The graph G is acyclically Llist colorable if there exists an acyclic coloring φ of G such that φ(v) ∈ L(v) for all v ∈ V (G). If G is acyclically Llist colorable for any list assignment L with L(v)  ≥ k for all v ∈ V (G), then G is acyclically kchoosable
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"... au titre de l’école doctorale de Mathématiques et Informatique de Bordeaux soutenue et présentée publiquement le 1er juillet 2013 ..."
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au titre de l’école doctorale de Mathématiques et Informatique de Bordeaux soutenue et présentée publiquement le 1er juillet 2013
Vertex decompositions of sparse graphs into an edgeless subgraph and a subgraph of maximum degree at most k
, 2010
"... A graph G is (k, 0)colorable if its vertices can be partitioned into subsets V1 and V2 such that in G[V1] every vertex has degree at most k, while G[V2] is edgeless. For every integer k ≥ 1, we prove that every graph with the maximum average degree smaller than 3k+4 is (k,0)colorable. k+2 In parti ..."
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Cited by 9 (6 self)
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A graph G is (k, 0)colorable if its vertices can be partitioned into subsets V1 and V2 such that in G[V1] every vertex has degree at most k, while G[V2] is edgeless. For every integer k ≥ 1, we prove that every graph with the maximum average degree smaller than 3k+4 is (k,0)colorable. k+2
Acyclic List 7Coloring Of Planar Graphs
 KOSTOCHKA, ANDRÉ RASPAUD, AND ÉRIC SOPENA. Acyclic
, 2001
"... . The acyclic list chromatic number of every 1planar graph is proved to be at most 7 and is conjectured to be at most 5. Keywords. Acyclic coloring, List coloring, Acyclic list coloring. 1 ..."
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Cited by 11 (1 self)
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. The acyclic list chromatic number of every 1planar graph is proved to be at most 7 and is conjectured to be at most 5. Keywords. Acyclic coloring, List coloring, Acyclic list coloring. 1
Honors
"... Research Interests – Discrete mathematics, combinatorics, and especially graph theory. – Coloring and list coloring of graphs, as well as variants of graph coloring. – The probabilistic method, the discharging method. ..."
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Research Interests – Discrete mathematics, combinatorics, and especially graph theory. – Coloring and list coloring of graphs, as well as variants of graph coloring. – The probabilistic method, the discharging method.
Results 1  10
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