Flows of 3-edge-colorable cubic signed graphs. (February 2023)

• Record Type: Journal Article
• Authors: Li, Liangchen; Li, Chong; Luo, Rong; Zhang, Cun-Quan; Zhang, Hailiang
• Is Part Of: European journal of combinatorics. Volume 108(2023)
• Publication Date: 2023-02
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2022.103627
• Languages: English
• ISSNs: 0195-6698

Abstract

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 3-edge-colorable cubic signed graph admits a nowhere-zero 10-flow. This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero 10-flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero 8-flow.