Flows on flow-admissible signed graphs
Matt DeVos, Jiaao Li, You Lu, Rong Luo, Cun-Quan Zhang, Zhang Zhang
TL;DR
This paper proves that all flow-admissible signed graphs admit a nowhere-zero 11-flow, improving previous bounds and advancing understanding of flow properties in signed graphs.
Contribution
The paper establishes that every flow-admissible signed graph admits a nowhere-zero 11-flow, significantly reducing the known upper bound from 30 and 216.
Findings
Every flow-admissible signed graph admits a nowhere-zero 11-flow
Improves the upper bound from 30 to 11 for such graphs
Advances the understanding of flow properties in signed graphs
Abstract
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero -flow. Bouchet himself proved that such signed graphs admit nowhere-zero -flows and Zyka further proved that such signed graphs admit nowhere-zero -flows. In this paper we show that every flow-admissible signed graph admits a nowhere-zero 11-flow.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Advanced Topology and Set Theory