Exact minimum degree thresholds for perfect matchings in uniform hypergraphs

Combinatorics Seminar
Friday, November 30, 2012 - 3:00pm
1 hour (actually 50 minutes)
Skiles 005
Georgia State University
Given integers k\ge 3 and d with k/2 \leq d \leq k-1, we give a minimum d-degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and extends the results of Pikhurko, R\"odl, Ruci\'{n}ski and Szemer\'edi. Our approach makes use of the absorbing method. This is a joint work with Andrew Treglown.