Ribbon graph minors and low-genus partial duals

TL;DR

This paper characterizes ribbon graphs that can be transformed into graphs of Euler genus at most one through partial duals, providing a clear criterion based on excluded minors.

Contribution

It offers the first excluded minor characterization for ribbon graphs with low-genus partial duals, advancing understanding of their structural properties.

Findings

Identifies specific minors that prevent low-genus partial duals.

Provides a complete classification of such ribbon graphs.

Establishes a foundation for further topological graph analysis.

Abstract

We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one.