Obstructions of Connectivity 2 for Embedding Graphs into the Torus

TL;DR

This paper identifies all minimal obstructions for embedding graphs into the torus with connectivity 2 and describes their building blocks for any orientable surface, advancing understanding of topological graph embeddings.

Contribution

It provides a complete characterization of obstructions for connectivity 2 graphs on the torus and generalizes to other orientable surfaces.

Findings

All obstructions for connectivity 2 on the torus are characterized.

Building blocks for obstructions on any orientable surface are described.

Advances understanding of graph embeddings in topological surfaces.

Abstract

The complete set of minimal obstructions for embedding graphs into the torus is still not determined. In this paper, we present all obstructions for the torus of connectivity 2. Furthermore, we describe the building blocks of obstructions of connectivity 2 for any orientable surface.