The Binomial k-Clique
Version of Record online: 1 OCT 2012
© 2012 Wiley Periodicals, Inc.
Journal of Combinatorial Designs
Volume 21, Issue 1, pages 36–45, January 2013
How to Cite
Narayana, N. S. and Sane, S. (2013), The Binomial k-Clique. J. Combin. Designs, 21: 36–45. doi: 10.1002/jcd.21333
- Issue online: 22 OCT 2012
- Version of Record online: 1 OCT 2012
- Manuscript Revised: 17 JUN 2012
- Manuscript Received: 16 SEP 2011
- maximal k-clique;
- binomial clique;
- projective plane;
- uniform hypergeraph
A finite collection C of k-sets, where is called a k-clique if every two k-sets (called lines) in C have a nonempty intersection and a k-clique is a called a maximal k-clique if and C is maximal with respect to this property. That is, every two lines in C have a nonempty intersection and there does not exist A such that , and for all . An elementary example of a maximal k-clique is furnished by the family of all the k-subsets of a -set. This k-clique will be called the binomial k-clique. This paper is intended to give some combinatorial characterizations of the binomial k-clique as a maximal k-clique. The techniques developed are then used to provide a large number of examples of mutually nonisomorphic maximal k-cliques for a fixed value of k.