Abstract
Let G be a graph with a perfect matching M. Define the forcing number of M in G to be the smallest size of a subset S⊂ M that is in no other perfect matching. In this paper, we present a property of bipartite graphs G that acts as a lower bound on the forcing number of perfect matchings in G. We then apply this to the torus and the hypercube, proving that the minimum forcing number of a perfect matching on a 2 m×2 n torus with m⩾ n is 2 n, and that the minimum forcing number on an n-dimensional hypercube is 2 n /4 if n is even.
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.
