Nowhere-zero 5-flow on signed ladders

2025/10/02 by Leila Parsaei Majd, Parsaei-Majd, Leila
Computer Science · #Advanced Data Storage Technologies #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Optimization and Search Problems

paper · pdf · doi:10.48550/arxiv.2510.01716

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero 6-flow. In this paper, we prove that Bouchet's conjecture holds for all signed ladders, circular and Möbius ladders. In fact, all signed ladders, circular and Möbius ladders admit a nowhere-zero 5-flow except for one case of signed circular ladders. Of course, the exception also has a nowhere-zero 6-flow.

Citations

• Nowhere-zero flows in signed graphs: A survey
• Signed graphs with two negative edges

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