Total choosability of planar graphs with maximum degree 4
نویسندگان
چکیده
منابع مشابه
k-forested choosability of graphs with bounded maximum average degree
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
متن کاملk-forested choosability of graphs with bounded maximum average degree
a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...
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It is proved that a planar graph with maximum degree ∆ ≥ 11 has total (vertex-edge) chromatic number ∆ + 1. c © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997
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The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we prove that, for planar graph G with maximum degree ∆ ≥ 12 and d = 2, the (2,1)-total labelling number λ2 (G) is at most ∆ + 2.
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Let G be a planar graph of maximum degree ∆ and girth g, and there is an integer t(> g) such that G has no cycles of length from g+1 to t. Then the total chromatic number of G is ∆+1 if (∆,g, t) ∈ {(5,4,6),(4,4,17)}; or ∆ = 3 and (g, t) ∈ {(5,13),(6,11),(7,11), (8,10),(9,10)}, where each vertex is incident with at most one g-cycle. 2010 Mathematics Subject Classification: 05C15
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.10.001