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arXiv · 2512.14285

Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor

Arnott Kidner·Eckhard Steffen·Weiqiang Yu
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Abstract

An $r$-regular graph is an $r$-graph, if every odd set of vertices is connected to its complement by at least $r$ edges. We prove for $r \in \{4,5\}$, every projective planar $r$-graph with no Petersen-minor is $r$-edge colorable.

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Arnott Kidner, Eckhard Steffen, Weiqiang Yu. 2025-12-16. Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. https://arxiv.org/abs/2512.14285

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