2014/02/12 by Daniel Horsley, Horsley, Daniel
Computer Science · Engineering · Mathematics · #05B07 (Primary) 05C51 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1402.2739
openalex publication_date 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was proved in 2009 that any partial Steiner triple system of order u has an embedding of order v for each admissible integer v≥ 2u+1. This result is best-possible in the sense that, for each u≥ 9, there exists a partial Steiner triple system of order u that does not have an embedding of order v for any v<2u+1. Many partial Steiner triple systems do have embeddings of orders smaller than 2u+1, but little has been proved about when these embeddings exist. In this paper we construct embeddings of orders less than 2u+1 for partial Steiner triple systems with few triples. In particular, we show that a partial Steiner triple system of order u ≥ 62 with at most (u2)/(50)-(11u)/(100)-(116)/(75) triples has an embedding of order v for each admissible integer v ≥ (8u+17)/(5).