Acyclic and oriented chromatic numbers of graphs
Journal of Graph Theory
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Graph colouring via the discharging method
Graph colouring via the discharging method
Acyclic colorings of subcubic graphs
Information Processing Letters
Acyclic edge colorings of graphs
Journal of Graph Theory
The acyclic edge chromatic number of a random d-regular graph is d + 1
Journal of Graph Theory
About acyclic edge colourings of planar graphs
Information Processing Letters
Acyclic edge coloring of graphs with maximum degree 4
Journal of Graph Theory
Random Structures & Algorithms
Optimal acyclic edge colouring of grid like graphs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Acyclic edge coloring of graphs
Discrete Applied Mathematics
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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) ⩽ Δ + 2, where Δ = Δ(G) denotes the maximum degree of the graph. If every induced subgraph H of G satisfies the condition |E(H)| ⩽ 2|V(H)|−1, we say that the graph G satisfies Property A. In this article, we prove that if G satisfies Property A, then a′(G) ⩽ Δ + 3. Triangle-free planar graphs satisfy Property A. We infer that a′(G) ⩽ Δ + 3, if G is a triangle-free planar graph. Another class of graph which satisfies Property A is 2-fold graphs (union of two forests). © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.