Acyclic Edge Coloring of 4-Regular Graphs Without 3-Cycles

A proper edge coloring is called acyclic if no bichromatic cycles are produced. It was conjectured that every simple graph G with maximum degree $$\varDelta $$Δ is acyclically edge-$$(\varDelta +2)$$(Δ+2)-colorable. Basavaraju and Chandran (J Graph Theory 61:192–209, 2009) confirmed the conjecture for non-regular graphs G with $$\varDelta =4$$Δ=4. In this paper, we extend this result by showing that every 4-regular graph G without 3-cycles is acyclically edge-6-colorable.

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