Seminar of Graph Theory - Edita Mačajová (13.3.2025)
Thursday 13.3.2025 at 9:50, Lecture room M 213
Edita Mačajová:
An 8-flow theorem for signed graphs
Abstract:
We show 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-colour 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.
This is a joint work with Rong Luo, Martin Skoviera, and Cun-Quan Zhang. The speaker is supported by VEGA 1/0727/22 and APVV-23-0076.