منابع مشابه
Acyclic 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 کاملAcyclic 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 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...
متن کاملAcyclic edge coloring of graphs
An acyclic edge coloring of a graph G is a proper edge coloring such that the subgraph induced by any two color classes is a linear forest (an acyclic graph with maximum degree at most two). The acyclic chromatic index χa(G) of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamčík (1978) conjectured that χa(G) ≤ ∆(G) + 2, where ∆(G) is the maximum degree of G...
متن کاملAcyclic list 7-coloring of planar graphs
Theacyclic list chromatic numberof every planar graph is proved to be at most 7. 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83–90, 2002
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/090776676