English

Flows of 3-edge-colorable cubic signed graphs

Combinatorics 2022-11-04 v1

Abstract

Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we proved that every flow-admissible 33-edge-colorable cubic signed graph admits a nowhere-zero 1010-flow. This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero 1010-flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero 88-flow.

Keywords

Cite

@article{arxiv.2211.01881,
  title  = {Flows of 3-edge-colorable cubic signed graphs},
  author = {Liangchen Li and Chong Li and Rong Luo and C. -Q Zhang and Hailing Zhang},
  journal= {arXiv preprint arXiv:2211.01881},
  year   = {2022}
}
R2 v1 2026-06-28T05:06:56.799Z