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- W2962961260 abstract "A strong k-edge-coloring of a graph G is a mapping from E(G) to {1,2,…,k} such that every pair of distinct edges at distance at most two receive different colors. The strong chromatic index χs′(G) of a graph G is the minimum k for which G has a strong k-edge-coloring. Denote σ(G)=maxxy∈E(G){deg(x)+deg(y)−1}. It is easy to see that σ(G)≤χs′(G) for any graph G, and the equality holds when G is a tree. For a planar graph G of maximum degree Δ, it was proved that χs′(G)≤4Δ+4 by using the Four Color Theorem. The upper bound was then reduced to 4Δ, 3Δ+5, 3Δ+1, 3Δ, 2Δ−1 under different conditions for Δ and the girth. In this paper, we prove that if the girth of a planar graph G is large enough and σ(G)≥Δ(G)+2, then the strong chromatic index of G is precisely σ(G). This result reflects the intuition that a planar graph with a large girth locally looks like a tree." @default.
- W2962961260 created "2019-07-30" @default.
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- W2962961260 date "2018-10-01" @default.
- W2962961260 modified "2023-09-26" @default.
- W2962961260 title "On the precise value of the strong chromatic index of a planar graph with a large girth" @default.
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- W2962961260 doi "https://doi.org/10.1016/j.dam.2018.03.075" @default.
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