Nowhere-zero 8-flows in cyclically 5-edge-connected, flow-admissible signed graphs

TL;DR

This paper proves that cyclically 5-edge-connected, flow-admissible signed graphs admit nowhere-zero 8-flows, advancing the understanding of flow values in such graphs and partially confirming Bouchet's conjecture.

Contribution

It establishes that for a specific class of signed graphs, the flow number can be improved from 216 to 8, providing a significant step toward Bouchet's conjecture.

Findings

Cyclically 5-edge-connected, flow-admissible signed graphs have nowhere-zero 8-flows.

The result narrows the gap toward Bouchet's conjecture for these graphs.

Advances the theory of flows in signed graphs.

Abstract

In 1983, Bouchet proved that every bidirected graph with a nowhere-zero integer-flow has a nowhere-zero 216-flow, and conjectured that 216 could be replaced with 6. This paper shows that for cyclically 5-edge-connected bidirected graphs that number can be replaced with 8.