On reverse Steiner triple systems
β Scribed by Alexander Rosa
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 950 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
1 he existence of reverse Steiner triple systems It.e. Steiner triple systems with a given involutory automorphism of speck4 type) is investigated. it is srfrwrn that such a system exists far alI wders n if n z t of 3 or 9 (mod 24: except posd&ly far n = 25. A system with this grspetty exists also for n = I9 md possibly for every n = 19 (mod 24). On the o:her hand, it is demonstmtcd that wch systems do not exist far the other values of II.
π SIMILAR VOLUMES
A Steiner triple system of order u is called reverse if its automorphism group contains an involution fixing only one point. We show mat such a system exists if and only if u = 1,3, 9 or 19 (mod 24).
## Abstract We study the list chromatic number of Steiner triple systems. We show that for every integer __s__ there exists __n__~0~=__n__~0~(__s__) such that every Steiner triple system on __n__ points STS(__n__) with __n__β₯__n__~0~ has list chromatic number greater than __s__. We also show that t
and v 15, a 3-chromatic Steiner triple system of order v all of whose 3-colorings are equitable. 1997 Academic Press ## 1. Introduction A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that eve