### DIMACS - Graduate Student Combinatorics Seminar

Title: The Size of a Hypergraph and its Matching Number

Speaker: **Brian Garnett**, Rutgers University

Date: Wednesday, February 15, 2012 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

This is the title of a recent paper (which I will summarize) by
Huang, Loh, and Sudakov. About 45 years ago, Erdos conjectured that
the size of a k-uniform hypergraph with less than t ( n/k) disjoint
edges has a certain upper bound and proved it for t O(n/k³). This paper improves the range to t O(n/k²). Next you guys can prove it for t n/k, and we'll be done with this!

Graduate Student Combinatorics Seminars