Circular flow number of highly edge connected signed graphs

TL;DR

This paper establishes a bound on the circular flow number for highly edge-connected signed graphs that are essentially unbalanced, linking graph connectivity with flow properties.

Contribution

It proves a new upper bound on the circular flow number for a class of highly edge-connected signed graphs based on their unbalancedness.

Findings

Circular flow number is at most 2+1/k for the specified graphs.

Higher edge connectivity implies tighter bounds on flow numbers.

Results extend understanding of flow properties in signed graphs.

Abstract

This paper proves that for any positive integer $k$, every essentially $(2k+1)$-unbalanced $(12k-1)$-edge connected signed graph has circular flow number at most $2+\frac 1k$.