Hamilton cycles in restricted block-intersection graphs

Abstract

As part of our main result we prove that the blocks of any sufficiently large BIBD(v, 4, ?) can be circularly ordered so that consecutive blocks intersect in exactly one point, i.e., that the 1-block-intersection graphs of such designs are Hamiltonian. In fact, we prove that such graphs are Hamilton-connected. We also consider {1, 2}-block-intersection graphs, in which adjacent vertices have either one or two points in common between their corresponding blocks. These graphs are Hamilton-connected for all sufficiently large BIBD(v, k, ?) with $${k \in \{4,5,6\}}$$ .