Five-coloring graphs on the Klein bottle

TL;DR

This paper provides a complete characterization of 5-colorable graphs on the Klein bottle through a specific list of nine forbidden subgraphs.

Contribution

It introduces an explicit list of nine graphs that precisely determine 5-colorability of graphs embedded in the Klein bottle.

Findings

A list of nine forbidden subgraphs for 5-colorability.

Characterization of 5-colorability via forbidden subgraphs.

Explicit criteria for Klein bottle graph coloring.

Abstract

We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list.