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Small embeddings for partial triple systems of odd index

✍ Scribed by Darryn Bryant; Geoffrey Martin


Book ID
113698796
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
365 KB
Volume
119
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES


Small embeddings for partial cycle syste
✍ C.C. Lindner; C.A. Rodger; D.R. Stinson πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 497 KB

We prove that if m is odd then a partial m-cycle system on n vertices can be embedded in an m-cycle system on at most m((m -2)n(n -1) + 2n + 1) vertices and that a partial weak Steiner m-cycle system on n vertices can be embedded in an m-cycle system on m(2n + 1) vertices.

A conjecture on small embeddings of part
✍ Darryn Bryant πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 106 KB πŸ‘ 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 Ο… for all υ ≑ 1 or 3, (mod 6), υ β‰₯ 2u + 1. However, some partial Steiner triple systems of order __u__ can be embedded in Steiner t

Small embeddings for partial 5-cycle sys
✍ Geoffrey Martin; Thomas A. McCourt πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 277 KB

## Abstract It has been conjectured that any partial 5‐cycle system of order __u__ can be embedded in a 5‐cycle system of order __v__ whenever **__v__**β‰₯**3****__u__/****2+1** and **__v__**≑**1****,****5 (mod 10)**. The smallest known embeddings for any partial 5‐cycle system of order __u__ is **10

A small embedding for partial even-cycle
✍ Peter Horak; C. C. Lindner πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 517 KB

Let m = 2k. We show that for some 0 ≀ < 1, a partial directed m-cycle system of order n can be embedded in a directed m-cycle system of order (mn)/2 + (2m 2 + 1) (8n + 1)/4 + 4m 3 2 + 4m + 1/2. For fixed m, this is asymptotic in n to (mn)/2 and so for large n is roughly one-fourth the best known bou

A proof of Lindner's conjecture on embed
✍ Darryn Bryant; Daniel Horsley πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 243 KB πŸ‘ 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. Β© 2008 Wiley Periodicals, Inc. J Combin Designs 17: 63–89, 2009