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- W2103337822 abstract "A proper edge coloring of G is r-acyclic if every cycle C contained in G is colored with at least min{|C|,r} colors. The r-acyclic chromatic index of a graph, denoted by ar′(G), is the minimum number of colors required to produce an r-acyclic edge coloring. In this paper, we study 4-acyclic edge colorings by proving that a4′(G)≤37Δ(G) for every planar graph, a4′(G)≤max{2Δ(G),3Δ(G)−4} for every series–parallel graph and a4′(G)≤2Δ(G) for every outerplanar graph. In addition, we prove that every planar graph with maximum degree at least r and girth at least 5r+1 has ar′(G)=Δ(G) for every r≥4." @default.
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- W2103337822 date "2012-09-01" @default.
- W2103337822 modified "2023-09-23" @default.
- W2103337822 title "On -acyclic edge colorings of planar graphs" @default.
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- W2103337822 doi "https://doi.org/10.1016/j.dam.2012.04.015" @default.
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