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The Existence Spectrum for Overlarge Sets of Pure Hybrid Triple Systems

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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 \(v>3\).

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Authors and Affiliations

  1. Department of Fundamental Science, North China Institute of Aerospace Engineering, Langfang, 065000, People’s Republic of China

    Yuanyuan Liu

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  1. Yuanyuan Liu
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Correspondence to Yuanyuan Liu.

Additional information

Research supported by Natural Science Foundation for the Youth 11101003, NSFC Grant 11171089.

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Liu, Y. The Existence Spectrum for Overlarge Sets of Pure Hybrid Triple Systems. Graphs and Combinatorics 32, 297–310 (2016). https://doi.org/10.1007/s00373-015-1567-9

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  • DOI: https://doi.org/10.1007/s00373-015-1567-9

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