Star edge-coloring of graphs with maximum degree four

Abstract The star chromatic index χ st ′ ( G ) of a graph G is the smallest integer k for which G has a proper k-edge-coloring without bichromatic paths or cycles of length four. In this paper, we prove that (1) if G is a graph with Δ = 4 , then χ st ′ ( G ) ≤ 14 ; and (2) if G is a bipartite graph with Δ = 4 , then χ st ′ ( G ) ≤ 13 .

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