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• W2247104300 abstract "The strong chromatic index of a graph $G$, denoted $chi'_s(G)$, is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted $chi'_{s,ell}(G)$, is the least integer $k$ such that if arbitrary lists of size $k$ are assigned to each edge then $G$ can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if $G$ is a subcubic planar graph with ${rm girth}(G) geq 41$ then $chi'_{s,ell}(G) leq 5$, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss. Math. Graph Theory, 33(4), (2014) 759--770]. We further show that if $G$ is a subcubic planar graph and ${rm girth}(G) geq 30$, then $chi_s'(G) leq 5$, improving a bound from the same paper.Finally, if $G$ is a planar graph with maximum degree at most four and ${rm girth}(G) geq 28$, then $chi'_s(G)N leq 7$, improving a more general bound of Wang and Zhao from [Odd graphs and its applications to the strong edge coloring, Applied Mathematics and Computation, 325 (2018), 246-251] in this case." @default.
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• W2247104300 date "2018-07-27" @default.
• W2247104300 modified "2023-10-16" @default.
• W2247104300 title "On the Strong Chromatic Index of Sparse Graphs" @default.
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• W2247104300 doi "https://doi.org/10.37236/5390" @default.
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