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Minimum embedding of Steiner triple systems into -designs II

✍ Scribed by Alan C.H. Ling; Charles J. Colbourn; Gaetano Quattrocchi


Book ID
108113977
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
745 KB
Volume
309
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


Embeddings of Steiner triple systems
✍ Jean Doyen; Richard M. Wilson πŸ“‚ Article πŸ“… 1973 πŸ› Elsevier Science 🌐 English βš– 867 KB

If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i

Minimum embedding of balanced P4-designs
✍ Gaetano Quattrocchi; Eric Mendelsohn πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 268 KB

A 5-cycle system on v + w points embeds a balanced P4-design on v points if there is a subset of v points on which the 5-cycles induce the blocks of a balanced P4-design. The mininum possible such w is v(mod 30) w v ≑ 4; 16 v -1 3 v ≑ 7; 10; 22; 25 v + 5 3 v ≑ 1; 13; 28 v + 11 3 v ≑ 19 (mod 30) v +

Surface embeddings of Steiner triple sys
✍ M. J. Grannell; T. S. Griggs; Jozef S˘irΓ‘n˘ πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 421 KB πŸ‘ 1 views

A Steiner triple system of order n (STS(n)) is said to be embeddable in an orientable surface if there is an orientable embedding of the complete graph Kn whose faces can be properly 2-colored (say, black and white) in such a way that all black faces are triangles and these are precisely the blocks

Minimum embedding of P3-designs into (K4
✍ Charles J. Colbourn; Alan C. H. Ling; Gaetano Quattrocchi πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 173 KB πŸ‘ 1 views

## Abstract A (__K__~4~β€‰βˆ’β€‰__e__)‐design on __v__ + __w__ points __embeds__ a __P__~3~‐design on __v__ points if there is a subset of __v__ points on which the __K__~4~β€‰βˆ’β€‰__e__ blocks induce the blocks of a __P__~3~‐design. It is shown that __w__ β‰₯ ¾(__v__β€‰βˆ’β€‰1). When equality holds, the embedding de

Quasi-embeddings of Steiner triple syste
✍ Peter Dukes; Eric Mendelsohn πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 182 KB

## Abstract In this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ ≑ 1,3 (mod 6), __u__ < __v__ < 2__u__ +  1, we ask for the minimum __r__ such that there exists a