The excluded minors for embeddability into a compact surface

TL;DR

This paper identifies the specific minimal obstructions, called excluded minors, that determine whether a countable graph can be embedded into a compact surface, advancing understanding of graph embedding properties.

Contribution

It provides a complete characterization of the excluded minors for embeddability of countable graphs into compact surfaces, a previously unresolved problem.

Findings

Identified all excluded minors for countable graph embeddability.

Established a characterization criterion for embeddability into compact surfaces.

Enhanced understanding of topological graph theory and surface embeddings.

Abstract

We determine the excluded minors characterising the class of countable graphs that embed into some compact surface.