Binomial partial Steiner triple systems containing complete graphs
Combinatorics
2014-10-30 v2
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.
Cite
@article{arxiv.1404.4064,
title = {Binomial partial Steiner triple systems containing complete graphs},
author = {M. Prażmowska and K. Prażmowski},
journal= {arXiv preprint arXiv:1404.4064},
year = {2014}
}
Comments
Corresponding author: M. Pra\.zmowska