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 $$v>3$$.