2014/04/15 by Małgorzata Prażmowska, Prażmowska, M., Krzysztof Prażmowski +1 · 1 citation
Engineering · Mathematics · #graph theory and CDMA systems #Finite Group Theory Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1404.4064
We propose a new approach to studies on partial Steiner triple systems consisting in determining complete graphs contained in them. We establish the structure which complete graphs yield in a minimal PSTS that contains them. As a by-product we introduce the notion of a binomial PSTS as a configuration with parameters of a minimal PSTS with a complete subgraph. A representation of binomial PSTS with at least a given number of its maximal complete subgraphs is given in terms of systems of perspectives. Finally, we prove that for each admissible integer there is a binomial PSTS with this number of maximal complete subgraphs.