Abstract
Vizing has shown that if G is a simple graph with maximum vertex-degree ϱ, then the chromatic index of G is either ϱ or ϱ + 1. In this note we prove that almost all graphs have a unique vertex of maximum degree, and we deduce that almost all graphs have chromatic index equal to their maximum degree. This settles a conjecture of the second author (in “Proceedings of the Fifth British Combinatorial Conference 1975”).
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.
