Nowhere-zero 3-flows in graphs admitting solvable arc-transitive groups of automorphisms

TL;DR

This paper proves that certain highly symmetric regular graphs with solvable automorphism groups admit nowhere-zero 3-flows, advancing understanding of Tutte's 3-flow conjecture in specific symmetric cases.

Contribution

It establishes that regular graphs of valency at least four with solvable arc-transitive automorphism groups have nowhere-zero 3-flows, a new result linking symmetry and flow properties.

Findings

Regular graphs with valency ≥ 4 and solvable automorphism groups admit nowhere-zero 3-flows.

The result applies to graphs with high symmetry, specifically those with solvable arc-transitive automorphism groups.

This work provides evidence supporting Tutte's 3-flow conjecture in symmetric graph classes.

Abstract

Tutte's 3-flow conjecture asserts that every 4-edge-connected graph has a nowhere-zero 3-flow. In this note we prove that every regular graph of valency at least four admitting a solvable arc-transitive group of automorphisms admits a nowhere-zero 3-flow.