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arXiv · 2511.09391

On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three

Gabriel Elvin·Hajrudin Fejzić·Youngsu Kim
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Abstract

We provide a simplified proof of the following special case of Wegner's conjecture: every planar graph of maximum degree at most three admits a distance-2 coloring with at most eight colors. Our main contribution is significant simplification of the most technically challenging part of Wegner's proof: the case involving the removal of a 5-cycle.

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Gabriel Elvin, Hajrudin Fejzić, Youngsu Kim. 2025-11-12. On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three. https://arxiv.org/abs/2511.09391

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