Acyclic edge coloring of planar graphs with large girth
نویسندگان
چکیده
منابع مشابه
Equitable coloring planar graphs with large girth
A proper vertex coloring of a graph G is equitable if the size of color classes differ by at most one. The equitable chromatic threshold of G, denoted by ∗Eq(G), is the smallest integer m such that G is equitably n-colorable for all n m. We prove that ∗Eq(G) = (G) if G is a non-bipartite planar graph with girth 26 and (G) 2 or G is a 2-connected outerplanar graph with girth 4. © 2007 Elsevier B...
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An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a(G). It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the gra...
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An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. In 1978, it was conjectured that ∆(G) + 2 colors suffice for an acyclic edge coloring of every graph G [6]. The conjecture has been verified for several classes of graphs, however, the best known upper bound for as special class as planar graphs are, is ∆+12 [2]. In this paper, we study simple planar graph...
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An edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every ε > 0, there exists a g = g(ε) such that if G has girth at least g then G admits an acyclic edge colouring with at most (1 + ε)∆ colours.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.08.015