Speaker : 1. Prof. Linyuan Lu(University of South Carolina) 2. Dr. Yu-Pei Huang ( I-Shou University)
Title : 1. Forbidden configurations and Repeated columns 2. On the Minimum Rank Problems of Graphs
Time : 2013-11-29 (Fri) 14:00 - 17:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: 1. How many edges can a simple hypergraph on vertices have when there is a forbidden configuration? A fundamental result is due to Sauer, Perles and Shelah, Vapnik and Chervonenkis. Let denote the complete hypergraph on vertices (with edges). Then any simple hypergraph on vertices forbidding can have at most edges. In this talk, we will consider the following forbidden configuration problem. Let be a given integer. Let be a family of subsets of . Assume that for every pair of disjoint sets with , there do not exist sets in where subsets of contain and are disjoint from and subsets of contain and are disjoint from . We show that is . This is joint work with Richard P. Anstee. 2. Let be a simple undirected graph on vertices. The matrices having as a described graph are the symmetric matrices indexed by the vertices of , whose off-diagonal entries are nonzero if the corresponding vertices are adjacent, and zero otherwise. The minimum rank of is defined as the minimum rank among these matrices. In this talk we will briefly introduce some current progress about the minimum rank problems. This is a joint work with Liang-Yu Hsieh.