Abstract
A triangle in a triple system is a collection of three edges isomorphic to {123,124,345}. A triple system is triangle-free if it contains no three edges forming a triangle. It is tripartite if it has a vertex partition into three parts such that every edge has exactly one point in each part. It is easy to see that every tripartite triple system is triangle-free. We prove that almost all triangle-free triple systems with vertex set [n] are tripartite. Our proof uses the hypergraph regularity lemma of Frankl and Rodl [13], and a stability theorem for triangle-free triple systems due to Keevash and the second author [15].
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.