arXiv:1404.4064 [math.CO]AbstractReferencesReviewsResources
Binomial partial Steiner triple systems containing complete graphs
Published 2014-04-15, updated 2014-10-28Version 2
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.
Comments: Corresponding author: M. Pra\.zmowska
Categories: math.CO
Related articles: Most relevant | Search more
arXiv:1706.00081 [math.CO] (Published 2017-05-31)
Two monads on the category of graphs
arXiv:1907.09165 [math.CO] (Published 2019-07-22)
Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations
arXiv:1002.3331 [math.CO] (Published 2010-02-17)
Spanning trees of 3-uniform hypergraphs