A new proof of Seymour's 6-flow theorem

TL;DR

This paper presents two alternative proofs of Seymour's 6-flow theorem, which states that every bridgeless graph admits a nowhere-zero 6-flow, providing new perspectives on a significant result in graph theory.

Contribution

It introduces two new proofs of Seymour's 6-flow theorem, offering alternative approaches that may enhance understanding and further research.

Findings

Two new proofs of Seymour's 6-flow theorem

Proofs are comparable in complexity to Seymour's original

Provides alternative perspectives on graph flows

Abstract

Tutte's famous 5-flow conjecture asserts that every bridgeless graph has a nowhere-zero 5-flow. Seymour proved that every such graph has a nowhere-zero 6-flow. Here we give (two versions of) a new proof of Seymour's Theorem. Both are roughly equal to Seymour's in terms of complexity, but they offer an alternative perspective which we hope will be of value.