Hamilton cycles in restricted block-intersection graphs

Authors:
Andrew T. Jesso;David A. Pike;Nabil Shalaby
Affiliations:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7;Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7;Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7
Venue:
Designs, Codes and Cryptography
Year:
2011

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Abstract

As part of our main result we prove that the blocks of any sufficiently large BIBD(v, 4, 驴) 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, 驴) with $${k \in \{4,5,6\}}$$ .