A representation of a set of maps as a ribbon bipartite graph

TL;DR

This paper explores representing a specific set of plane maps as ribbon bipartite graphs to estimate their genus, providing a novel experimental approach to understanding their topological properties.

Contribution

It introduces a new experimental method to model plane maps as ribbon bipartite graphs for genus estimation.

Findings

Successful representation of plane maps as ribbon bipartite graphs.

Effective estimation of the genus of the initial set of maps.

Potential for applying this method to other classes of maps.

Abstract

In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.