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arXiv · 1404.4064

Binomial partial Steiner triple systems containing complete graphs

M. Prażmowska·K. Prażmowski
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Abstract

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.

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M. Prażmowska, K. Prażmowski. 2014-10-28. Binomial partial Steiner triple systems containing complete graphs. https://arxiv.org/abs/1404.4064

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