Bouchet's conjecture for cyclically 5-edge-connected, cubic signed graphs
Kathryn Nurse
TL;DR
This paper proves Bouchet's 1983 conjecture that every flow-admissible signed graph has a nowhere-zero six-flow, specifically for cyclically five-edge-connected, cubic signed graphs.
Contribution
It provides the first proof of Bouchet's conjecture for a significant class of signed graphs, advancing understanding in graph flow theory.
Findings
Bouchet's conjecture holds for cyclically five-edge-connected, cubic signed graphs.
The proof confirms the conjecture in a previously unresolved case.
Results contribute to the broader theory of flows in signed graphs.
Abstract
A 1983 conjecture of Bouchet states that every flow-admissible signed graph has a nowhere-zero six-flow. We prove this conjecture for cyclically five-edge-connected, cubic signed graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Geometric and Algebraic Topology