A short proof of Seymour's 6-flow theorem

TL;DR

This paper presents a concise variation of Seymour's proof demonstrating that every 2-edge-connected graph admits a specific type of nowhere-zero flow, simplifying the understanding of this fundamental graph theory result.

Contribution

It provides a more compact and accessible proof of Seymour's 6-flow theorem, enhancing clarity and understanding of the original result.

Findings

Every 2-edge-connected graph has a nowhere-zero  -flow.

The proof is more compact and easier to understand.

Supports the validity of Seymour's 6-flow theorem.

Abstract

We give a compact variation of Seymour's proof that every $2$-edge-connected graph has a nowhere-zero $\mathbb{Z}_2 \times \mathbb{Z}_3$-flow.