Minimum embedding of Steiner triple systems into -designs II
β 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
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
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 β‘ 4; 16 v -1 3 v β‘ 7; 10; 22; 25 v + 5 3 v β‘ 1; 13; 28 v + 11 3 v β‘ 19 (mod 30) v +
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
## Abstract A (__K__~4~βββ__e__)βdesign on __v__β+β__w__ points __embeds__ a __P__~3~βdesign on __v__ points if there is a subset of __v__ points on which the __K__~4~βββ__e__ blocks induce the blocks of a __P__~3~βdesign. It is shown that __w__ββ₯βΒΎ(__v__βββ1). When equality holds, the embedding de
## Abstract In this paper, we present a conjecture that is a common generalization of the DoyenβWilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ β‘ 1,3 (mod 6), __u__ < __v__ < 2__u__β+β 1, we ask for the minimum __r__ such that there exists a