Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4. Issue 2 (20th June 2016)

• Record Type: Journal Article
• Authors: Mazzuoccolo, Giuseppe; Steffen, Eckhard
• Is Part Of: Journal of graph theory. Volume 85:Issue 2(2017)
• Page Start: 363
• Page End: 371
• Publication Date: 2016-06-20
• Subjects: 5‐flow conjecture -- nowhere‐zero flows -- cubic graphs -- oddness of cubic graphs -- Tutte's flow conjectures; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22065
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6.