Title:
3-Uniform Friendship Hypergraphs
Date:
Thursday, March 17, 2011 at 1:00pm
Location:
E2-304 EITC Building, University of Manitoba Fort Garry Campus
Speaker:
Dr. John van Rees
Department of Computer Science, University of Manitoba
Abstract:
The well-known Friendship Theorem states that if a graph in which every pair
of vertices has exactly one common neighbour, then G has a single vertex joined to all others, “a universal friend”. V. Sos defined the following friendship property for 3-uniform hypergraphs (every edge has 3 vertices). For every three vertices, x, y and z there exists a unique vertex w such that xyw, yzw and xzw are all edges in the 3-hypergraph. She showed constructions featuring “a universal friend. Hartke and Vandenbussche showed constructions for 8, 16 and 32 vertices. We improve the bounds on the size of a 3-uniform friendship hypergraph. We also put the problem in a geometrical setting. We prove that the 3 hypergraphs found on 16 points are geometrical and are the only geometrical hypergraphs on 16 points.
Cost:
This will be a free event.
Contact:
If you would like additional information or if you might be interested in presenting a seminar, please contact Steph Durocher or the Department of Computer Science.
