Excluded checkerboard colourable ribbon graph minors

TL;DR

This paper introduces new concepts of checkerboard colourable minors and bipartite minors for ribbon graphs, providing an excluded minor characterization for these classes and their planar variants.

Contribution

It defines checkerboard colourable and bipartite minors for ribbon graphs and characterizes these classes via excluded minors, extending classical graph minor theory.

Findings

Provides a characterization of checkerboard colourable ribbon graphs.

Establishes excluded minor theorems for bipartite ribbon graphs.

Extends minor theory to ribbon graphs with planar cases.

Abstract

In this paper, we first introduce the notions of checkerboard colourable minors for ribbon graphs motivated by the Eulerian ribbon graph minors, and two kinds of bipartite minors for ribbon graphs, one of which is the dual of the checkerboard colourable minors and the other is motivated by the bipartite minors of abstract graphs. Then we give an excluded minor characterization of the class of checkerboard colourable ribbon graphs, bipartite ribbon graphs, plane checkerboard colourable ribbon graphs and plane bipartite ribbon graphs.