1. An 8-flow theorem for signed graphs
- Author
-
Luo, Rong, Máčajová, Edita, Škoviera, Martin, and Zhang, Cun-Quan
- Subjects
Mathematics - Combinatorics ,05C22, 05C21 - Abstract
We prove that a signed graph admits a nowhere-zero $8$-flow provided that it is flow-admissible and the underlying graph admits a nowhere-zero $4$-flow. When combined with the 4-color theorem, this implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero $8$-flow. Our result improves and generalizes previous results of Li et al. (European J. Combin. 108 (2023), 103627), which state that every flow-admissible signed $3$-edge-colorable cubic graph admits a nowhere-zero $10$-flow, and that every flow-admissible signed hamiltonian graph admits a nowhere-zero $8$-flow., Comment: 12 pages, 2 figures
- Published
- 2024