A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane

TL;DR

This paper presents a constructive proof of the strong Hanani-Tutte theorem on the projective plane, offering a potential pathway to extend similar results to other surfaces and enabling efficient algorithms for embeddings.

Contribution

The authors provide a new constructive proof that does not depend on forbidden minor characterization, facilitating extensions to other surfaces and practical algorithms.

Findings

Proof is constructive and does not rely on forbidden minors

Method can be extended to other surfaces

Enables efficient algorithms for embeddings

Abstract

We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives hope to extend it to other surfaces. Moreover, our approach can be used to provide an efficient algorithm turning a Hanani-Tutte drawing on the projective plane into an embedding.