Nowhere-zero 8-flows in 3-edge-connected signed graphs
Matt DeVos, Kathryn Nurse, Robert \v{S}\'amal
TL;DR
This paper proves that every 3-edge-connected flow-admissible signed graph admits a nowhere-zero 8-flow, extending previous results and supporting Bouchet's conjecture for this class of graphs.
Contribution
It establishes that all 3-edge-connected flow-admissible signed graphs have a nowhere-zero 8-flow, advancing the understanding of flow properties in signed graphs.
Findings
Every 3-edge-connected flow-admissible signed graph has a nowhere-zero 8-flow.
Extends previous results to a broader class of signed graphs.
Supports Bouchet's conjecture for 3-edge-connected signed graphs.
Abstract
In 1983, A. Bouchet extended W.T. Tutte's notion of nowhere-zero flows to signed graphs, and conjectured that every flow-admissible signed graph has a nowhere-zero 6-flow. In this paper we prove that every flow-admissible signed graph that is 3-edge-connected has a nowhere-zero 8-flow. This is a continuation of a previous paper where we proved the same conclusion under stronger assumptions.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Complexity and Algorithms in Graphs