On block-schematic Steiner systems $S(t,t+2,v)$ and $S(t,t+3,v)$
نویسندگان
چکیده
منابع مشابه
Block-Intersection Graphs of Steiner Triple Systems
A Steiner triple system of order n is a collection of subsets of size three, taken from the n-element set {0, 1, ..., n−1}, such that every pair is contained in exactly one of the subsets. The subsets are called triples, and a block-intersection graph is constructed by having each triple correspond to a vertex. If two triples have a non-empty intersection, an edge is inserted between their vert...
متن کاملOn the Block Coloring of Steiner Triple Systems
A Steiner triple system of order v, STS(v), is an ordered pair S = (V,B), where V is a set of size v and B is a collection of triples of V such that every pair of V is contained in exactly one triple of B. A k-block coloring is a partitioning of the set B into k color classes such that every two blocks in one color class do not intersect. In this paper, we introduce a construction and use it to...
متن کاملBlock transitive Steiner systems with more than one point orbit
For all ‘reasonable’ finite t, k and s we construct a t-(א0, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2-(א0, 4, 1) design with a block-transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial wa...
متن کاملHamilton Decompositions of Block-Intersection Graphs of Steiner Triple Systems
Block-intersection graphs of Steiner triple systems are considered. We prove that the block-intersection graphs of non-isomorphic Steiner triple systems are themselves non-isomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable block-intersection graph.
متن کاملDecomposing block-intersection graphs of Steiner triple systems into triangles
The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd degree is necessary before the rest can be decomposed into triangles. In this case, some decompos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1990
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381517494