Equitable colorings of planar graphs with maximum degree at least nine
نویسندگان
چکیده
منابع مشابه
Total colorings of planar graphs with large maximum degree
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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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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We consider the problem of list edge coloring for planar graphs. Edge coloring is the problem of coloring the edges while ensuring that two edges that are incident receive different colors. A graph is k-edge-choosable if for any assignment of k colors to every edge, there is an edge coloring such that the color of every edge belongs to its color assignment. Vizing conjectured in 1965 that every...
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The total chromatic number of a graph G, denoted by χ′′(G), is the minimum number of colors needed to color the vertices and edges of G such that no two adjacent or incident elements get the same color. It is known that if a planar graph G has maximum degree ∆ > 9, then χ′′(G) = ∆ + 1. The join K1 ∨ Pn of K1 and Pn is called a fan graph Fn. In this paper, we prove that if G is an F5-free planar...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.11.004