Abstract

AbstractConsider the random process in which the edges of a graph are added one by one in a random order. A classical result states that if is the complete graph or the complete bipartite graph , then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary ‐regular bipartite graphs on vertices for all . Surprisingly, this is not the case for smaller values of . Using a construction due to Goel, Kapralov, and Khanna, we show that there exist bipartite ‐regular graphs in which the last isolated vertex disappears long before a perfect matching appears.

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 call

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.