Acyclic Edge Coloring of Triangle-Free Planar Graphs
نویسندگان
چکیده
منابع مشابه
Acyclic Edge Coloring of Triangle Free Planar Graphs
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...
متن کاملEdge Coloring of Triangle-Free 1-Planar Graphs
it is shown that each triangle-free 1-planar graph with maximum degree $\Delta\geq7$ can be $\Delta$-colorable by Discharging Method.
متن کاملAcyclic Edge coloring of Planar Graphs
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...
متن کاملFractional Coloring of Triangle-Free Planar Graphs
We prove that every planar triangle-free graph on n vertices has fractional chromatic number at most 3− 1 n+1/3 .
متن کاملAcyclic edge coloring of planar graphs with Δ colors
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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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20651