Another proof of Seymour's 6-flow theorem

TL;DR

This paper presents a new, concise proof of a generalized version of Seymour's 6-flow theorem, extending its applicability to functions with specific boundary constraints on 2-edge-connected graphs.

Contribution

It introduces a simplified proof of a broader theorem, expanding Seymour's original 6-flow result to include boundary-constrained functions.

Findings

New short proof of generalized 6-flow theorem

Extension to boundary-constrained functions

Applicable to all 2-edge-connected graphs

Abstract

In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group ${\mathbb Z}_2 \times {\mathbb Z}_3$ (in fact, he offers two proofs of this result). In this note we give a new short proof of a generalization of this theorem where ${\mathbb Z}_2 \times {\mathbb Z}_3$-valued functions are found subject to certain boundary constraints.