Abstract
We develop four constructions for nowhere-zero 5-flows of 3-regular graphs that satisfy special structural conditions. Using these constructions we show a minimal counter-example to Tutte's 5-Flow Conjecture is of order ≥44 and therefore every bridgeless graph of nonorientable genus ≤5 has a nowhere-zero 5-flow. One of the structural properties is formulated in terms of the structure of the multigraph G(F) obtained from a given 3-regular graph G by contracting the cycles of a 2-factor F in G. © 1996 John Wiley & Sons, Inc.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
