Another proof of the result on rotation compatible planar covers

Shohei Koizumi; Yusuke Suzuki; Kensuke Tamura

Another proof of the result on rotation compatible planar covers

Combinatorics 2026-06-26 v1

Authors: Shohei Koizumi , Yusuke Suzuki , Kensuke Tamura

Abstract

Negami's Planar Cover Conjecture asserts that a connected graph has a finite planar cover if and only if it can be embedded on the projective plane. While this statement has already been proven for rotation compatible planar covers, namely covers equipped with a certain condition on the rotation system, the existing proof relies on advanced algebraic and topological methods. In this paper, we provide another proof of this result, focusing primarily on combinatorial arguments based on a structural analysis with respect to a spanning tree in the base graph.

Keywords

planar covers Negami's conjecture rotation compatible projective plane combinatorial proof

Cite

@article{arxiv.2606.27703,
  title  = {Another proof of the result on rotation compatible planar covers},
  author = {Shohei Koizumi and Yusuke Suzuki and Kensuke Tamura},
  journal= {arXiv preprint arXiv:2606.27703},
  year   = {2026}
}