Abstract
AbstractA bisection of a graph is a bipartition of its vertex set in which the two classes differ in size by at most one. For a random bisection of a graph with edges, one expects edges spans in one vertex class. Bollobás and Scott asked for conditions that guarantee a bisection in which both classes span at most edges simultaneously. Let be integers with , and let be a graph with minimum degree and edges. In this article, we prove that if contains neither triangle nor as a subgraph, then admits a bisection in which both classes span at most edges. We also consider Max‐Bisections of graphs without and improve a recent result of Hou and Yan.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.