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2024-02-15 07:12:40

Edge coloring lattice graphs
Joris Kattem\"olle
https://arxiv.org/abs/2402.08752 https://arxiv.org/pdf/2402.08752

Edge coloring lattice graphs
We develop the theory of the edge coloring of infinite lattice graphs, proving a necessary and sufficient condition for a proper edge coloring of a patch of a lattice graph to induce a proper edge coloring of the entire lattice graph by translation. This condition forms the cornerstone of a method that finds nearly minimal or minimal edge colorings of infinite lattice graphs. In case a nearly minimal edge coloring is requested, the running time is $O(μ^2 D^4)$, where $μ$ is the number of edge…