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The Existence Spectrum for Overlarge Sets of Pure Hybrid Triple Systems

Research paper by Yuanyuan Liu

Indexed on: 05 Apr '15Published on: 05 Apr '15Published in: Graphs and Combinatorics



Abstract

An overlarge set of pure Hybrid triple system \((PHTS)\), denoted by \(OLPHTS(v)\), is a collection \(\{(Y{\setminus }\{y_i\},{\mathcal {A}}_i)\}_i\), where \(Y\) is a \((v+1)\)-set, \(y_i\in Y\), each \((Y{\setminus }\{y_i\},{\mathcal {A}}_i)\) is a \(PHTS(v)\) and these \({\mathcal {A}}_i\)s form a partition of all cyclic triples and transitive triples on \(Y.\) In this paper, we shall discuss the existence problem of \(OLPHTSs\) and get the following conclusion: there exists an \(OLPHTS(v)\) if and only if \(v\equiv 0,1\) mod 3 and \(v>3\).