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arXiv · 2208.02579

Cycle space of graphs of polytopes

Guillermo Pineda-Villavicencio
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Abstract

It is folklore that the cycle space of graphs of polytopes is generated by the cycles bounding the 2-faces. We provide a proof of this result that bypass homological arguments, which seem to be the most widely known proof. As a corollary, we obtain a result of Blind & Blind (1994) stating that graphs of polytopes are bipartite if and only if graphs of every 2-face are bipartite.

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Guillermo Pineda-Villavicencio. 2022-08-04. Cycle space of graphs of polytopes. https://arxiv.org/abs/2208.02579

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