Abstract
A perfect matching in a 4-uniform hypergraph on n vertices is a subset of ⌊n4⌋ disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph on n=4k vertices such that every vertex belongs to more than (n−13)−(3n/43) edges, then H contains a perfect matching. A construction due to Hàn, Person, and Schacht shows that this result is the best possible.
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.