共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Daniel Horsley 《组合设计杂志》2014,22(8):343-365
It was proved in 2009 that any partial Steiner triple system of order u has an embedding of order v for each admissible . This result is best possible in the sense that, for each , there exists a partial Steiner triple system of order u that does not have an embedding of order v for any . Many partial Steiner triple systems do have embeddings of orders smaller than , but much less is known about when these embeddings exist. In this paper, we detail a method for constructing such embeddings. We use this method to show that each member of a wide class of partial Steiner triple systems has an embedding of order v for at least half (or nearly half) of the orders for which an embedding could exist. For some members of this class we are able to completely determine the set of all orders for which the member has an embedding. 相似文献
3.
4.
A Steiner pentagon system is a pair (Kn, P) where Kn isthe complete undirected graph on n vertices. P is a collection of edge-disjoint pentagons which partition Kn, and such that every part of distinct vertices of Kn is joined by a path of length two in exactly one pentagon of the collection P. The number n is called the order of the system. This paper gives a somplete solution of the existence problem of Steiner pentagon systems. In particular it is shown that the spectrum for Steiner pentagon systems (=the set of all orders for which a Steiner pentagon system exists) is precisely the set of all n ≡ 1 or 5 (mod 10), except 15, for which no such system exists. 相似文献
5.
6.
R.J.R. Abel 《Discrete Applied Mathematics》2008,156(5):780-793
A Steiner pentagon system of order v(SPS(v)) is said to be super-simple if its underlying (v,5,2)-BIBD is super-simple; that is, any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary condition for the existence of a super-simple SPS(v); namely, v?5 and v≡1 or is sufficient, except for v=5, 15 and possibly for v=25. In the process, we also improve an earlier result for the spectrum of super-simple (v,5,2)-BIBDs, removing all the possible exceptions. We also give some new examples of Steiner pentagon packing and covering designs (SPPDs and SPCDs). 相似文献
7.
Chu Wensong 《数学学报(英文版)》1998,14(1):135-138
In this paper, we completely solve the embedding problem of simple directed triple systems by proving that the necessary conditions
for the embeddings of directed triple systems are also sufficient.
This project is supported by the Science and Technology Foundation of Shanghai Jiao Tong University 相似文献
8.
In this article it is shown that any resolvable Mendelsohn triple system of order u can be embedded in a resolvable Mendelsohn triple system of order v iff v≥ 3u, except possibly for 71 values of (u,v). © 1993 John Wiley & Sons, Inc. 相似文献
9.
10.
A partial Steiner (k,l)-system is a k-uniform hypergraph
with the property that every l-element subset of V is contained in at most one edge of
. In this paper we show that for given k,l and t there exists a partial Steiner (k,l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of this note, we establish asymptotic lower and upper bounds on the size of such cliques with respect
to the order of Steiner systems.
Research of the second author partially supported by NSERC grant OGP0025112. 相似文献
11.
In this article, it is shown that the necessary conditions for the existence of a holey Steiner pentagon system (HSPS) of type hn are also sufficient, except possibly for the following cases: (1) when n = 15, and h ≡ 1 or 5 (mod 6) where h ≢ 0 (mod 5), or h = 9; and (2) (h, n) ∈ {(6, 6), (6, 36), (15, 19), (15, 23), (15, 27), (30, 18), (30, 22), (30, 24)}. Moreover, the results of this article guarantee the analogous existence results for group divisible designs (GDDs) of type hn with block-size k = 5 and index λ = 2. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 41–56, 1999 相似文献
12.
A Steiner system S(l, m, n) is a system of subsets of size m (called blocks) from an n-set S, such that each d-subset from S is contained in precisely one block. Two Steiner systems have intersection k if they share exactly k blocks. The possible intersections among S(5, 6, 12)'s, among S(4, 5, 11)'s, among S(3, 4, 10)'s, and among S(2, 3, 9)'s are determined, together with associated orbits under the action of the automorphism group of an initial Steiner system. The following are results: (i) the maximal number of mutually disjoint S(5, 6, 12)'s is two and any two such pairs are isomorphic; (ii) the maximal number of mutually disjoint S(4, 5, 11)'s is two and any two such pairs are isomorphic; (iii) the maximal number of mutually disjoint S(3, 4, 10)'s is five and any two such sets of five are isomorphic; (iv) a result due to Bays in 1917 that there are exactly two non-isomorphic ways to partition all 3-subsets of a 9-set into seven mutually disjoint S(2, 3, 9)'s. 相似文献
13.
Alan C. H. Ling 《Journal of Geometry》2003,77(1-2):129-135
In this paper, we show that the basic necessary condition for the existence of a (k; 0, 2)-set in an
S(2, 4, v) is also sufficient. It solves a problem posed by de Resmini [6] and we also prove some asymptotic
results concerning the existence of hyperovals in Steiner systems with large block size. The results are generally
applicable to designs with maximal arcs. 相似文献
14.
Michel Dehon 《Journal of Geometry》1979,12(1):1-9
A regular planar Steiner triple system is a Steiner triple system provided with a family of non-trivial sub-systems of the same cardinality (called planes) such that (i) every set of 3 non collinear points is contained in exactly one plane and (ii) for every plane H and every disjoint block B, there are exactly planes containing B and intersecting H in a block. We prove that a regular planar Steiner triple system is necessarily a projective space of dimension greater than 2 over GF(2), the 3-dimensional affine space over GF(3), an S(2, 3, 2 (6m+7) (3m2+3m+1)+1) with m1, an S(2, 3, 171), an S(2, 3, 183) or an S(2, 3, 2055). 相似文献
15.
16.
17.
A two-fold pentagon system is a decomposition of the complete 2-multigraph (every two distinct vertices joined by two edges) into pentagons. A two-fold Steiner pentagon system is a two-fold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. We consider two-fold Steiner pentagon systems with an additional property : for any two vertices, the two paths of length two joining them are distinct. We determine completely the spectrum for such systems, and point out an application of such systems to certain 4-cycle systems. 相似文献
18.
Alice Devillers 《组合设计杂志》2003,11(3):153-161
A Steiner system (or t — (v, k, 1) design) S is said to be homogeneous if, whenever the substructures induced on two finite subsets S1 and S2 of S are isomorphic, there is at least one automorphism of S mapping S1 onto S2, and is said to be ultrahomogeneous if each isomorphism between the substructures induced on two finite subsets of S can be extended to an automorphism of S. We give a complete classification of all homogeneous and ultrahomogeneous Steiner systems. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 153–161, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10034 相似文献
19.
20.
A partial Steiner triple system of order is sequenceable if there is a sequence of length of its distinct points such that no proper segment of the sequence is a union of point‐disjoint blocks. We prove that if a partial Steiner triple system has at most three point‐disjoint blocks, then it is sequenceable. 相似文献