Existential closure of block intersection graphs of infinite designs having infinite block size

Abstract

A graph G is n-existentially closed (n-e.c.) if for each pair (A, B) of disjoint subsets of V(G) with |A| + |B|≤n there exists a vertex in V(G)\(A∪B) which is adjacent to each vertex in A and to no vertex in B. In this paper we study the n-existential closure property of block intersection graphs of infinite designs with infinite block size. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:317-327, 2011