Speaker: Dr. David Pike, Department of Mathematics and Statistics, Memorial University
A graph G with vertex set V is said to be n-existentially closed (or n-e.c. for short) if, for every proper subset S of V with |S|=n and every subset T of S, there exists a vertex x in V-S such that x is adjacent to each vertex of T but is adjacent to no vertex of S-T.
A balanced incomplete block design (
BIBD) with parameters (v,k,lambda) consists of a set of blocks, each of which is a k-subset of a set V of cardinality v, such that each 2-subset of V occurs in precisely lambda of the blocks of the design.
Given a combinatorial design D with block set B, its block-intersection graph is the graph having B as its vertex set, such that two vertices b_1 and b_2 are adjacent if and only if b_1 and b_2 have non-empty intersection.
In this talk we will present some recent results concerning balanced incomplete block designs (BIBDs) and when their block-intersection graphs are n-existentially closed.
This is joint work with Neil A. McKay.
About the speaker:
David Pike is n Associate Professor in the
Department of Mathematics and Statistics and the Department of Computer Science at Memorial University, St. John’s, NL. He received his Ph.D. in Discrete Mathematics from Auburn University, Auburn, Alabama. His current research include: cycle systems and graph decompositions, block-intersection graphs of combinatorial designs, computational problems in graph theory and combinatorics, phylogenetic networks, identifying clusters of related nodes in information networks, and applications of graph theory to population genetics and ecological connectivity.
