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 -edge-colorable cubic signed graph admits a nowhere-zero -flow. This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero -flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero -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}
}