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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 ${\chi_{\ell,s}''(G)}$, 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 $\operatorname{girth}(G) \geq 41$ then ${\chi_{\ell,s}''(G)}\leq 5$, 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 $\operatorname{girth}(G) \geq 30$, 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 $\operatorname{girth}(G) \geq 28$, then ${\chi_{s}''(G)}\leq 7$, improving a more general bound of Wang and Zhao from \[Odd graphs and its application on the strong edge coloring, `arXiv:1412.8358`\] in this case.'
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