DEPARTMENT OF MATHEMATICS
       ALGEBRA AND COMBINATORICS SEMINAR

  12 noon THURSDAY 28 OCTOBER 2004  in 67-641


   Pancyclic BIBD Block-Intersection Graphs

               David A. Pike
      Memorial University of Newfoundland


Abstract
 
Given a combinatorial design  D  with block set  B, its
block-intersection graph  G_D  is the graph having vertex
set  B  such that two vertices  b_1  and  b_2  are adjacent 
if and only if  b_1  and  b_2  have non-empty intersection.
Alspach and Hare proved that if  D  is a balanced incomplete
block design, BIBD(v,k,1)  with  k \geq 3,
then  G_D  is edge-pancyclic
(i.e. each edge of  G_D  is contained in a cycle of each length
\ell = 3,4,...,|V(G_D)|).
In this paper, it is proved that if  D  is a
BIBD(v,k,\lambda)  with arbitrary index  \lambda \geq 2,
then  G_D  is pancyclic
(i.e.  G_D  contains a cycle of each length
\ell = 3,4,...,|V(G_D)|).


This is joint work with Aygul Mamut (Xinjiang University, China)
and Michael Raines (Western Michigan University).




All welcome.