Six‐flows on almost balanced signed graphs. Issue 4 (17th April 2019)

• Record Type: Journal Article
• Authors: Wang, Xiao; Lu, You; Zhang, Cun‐Quan; Zhang, Shenggui
• Is Part Of: Journal of graph theory. Volume 92:Issue 4(2019)
• Page Start: 394
• Page End: 404
• Publication Date: 2019-04-17
• Subjects: frustration number -- integer flow -- signed graph; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22460
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: In 1983, Bouchet conjectured that every flow‐admissible signed graph admits a nowhere‐zero 6‐flow. By Seymour's 6‐flow theorem, Bouchet's conjecture holds for signed graphs with all edges positive. Recently, Rollová et al proved that every flow‐admissible signed cubic graph with two negative edges admits a nowhere‐zero 7‐flow, and admits a nowhere‐zero 6‐flow if its underlying graph either contains a bridge, or is 3‐edge‐colorable, or is critical. In this paper, we improve and extend these results, and confirm Bouchet's conjecture for signed graphs with frustration number at most two, where the frustration number of a signed graph is the smallest number of vertices whose deletion leaves a balanced signed graph.