𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Uniform two-class regular partial Steiner triple systems

✍ Scribed by Melissa S. Keranen; Donald L. Kreher; Sibel Özkan

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
156 KB
Volume
20
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A 2‐class regular partial Steiner triple system is a partial Steiner triple system whose points can be partitioned into 2‐classes such that no triple is contained in either class and any two points belonging to the same class are contained in the same number of triples. It is uniform if the two classes have the same size. We provide necessary and sufficient conditions for the existence of uniform 2‐class regular partial Steiner triple systems.

📜 SIMILAR VOLUMES

Steiner triple systems with two disjoint
Steiner triple systems with two disjoint subsystems
✍ Darryn Bryant; Daniel Horsley 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB

## Abstract It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order __v__ by removing the edges of two vertex disjoint complete subgraphs of orders __u__ and __w__ if and only if __u,w__, and __v__ are odd, ${{v}\choose 2}-{u\choose 2}- {w\choos

A conjecture on small embeddings of part
A conjecture on small embeddings of partial Steiner triple systems
✍ Darryn Bryant 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 106 KB 👁 1 views

## Abstract A well‐known, and unresolved, conjecture states that every partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order υ for all υ ≡ 1 or 3, (mod 6), υ ≥ 2u + 1. However, some partial Steiner triple systems of order __u__ can be embedded in Steiner t

Embedding partial Steiner triple systems
Embedding partial Steiner triple systems so that their automorphisms extend
✍ Peter J. Cameron 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB

It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on v v v points, in such a way that all automorphisms of U can be extended to V, for every admissible v v v satisfying v v v > gðuÞ. We f

Infinite classes of anti-mitre and 5-spa
Infinite classes of anti-mitre and 5-sparse Steiner triple systems
✍ Yuichiro Fujiwara 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 135 KB 👁 1 views

## Abstract In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class mod

A proof of Lindner's conjecture on embed
A proof of Lindner's conjecture on embeddings of partial Steiner triple systems
✍ Darryn Bryant; Daniel Horsley 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB 👁 1 views

## Abstract Lindner's conjecture that any partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order __v__ if $v\equiv 1,3 \; ({\rm mod}\; 6)$ and $v\geq 2u+1$ is proved. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 63–89, 2009