منابع مشابه
Bicoloring Steiner Triple Systems
A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give a multiplication theorem for Steiner triple systems with 3 color classes. We also examine bicolo...
متن کاملBalanced Steiner Triple Systems
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 every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map , : X [1, ..., r] such that at least two...
متن کاملCliques in Steiner Systems
A partial Steiner (k, l)-system is a k-uniform hypergraph G with the property that every l-element subset of V is contained in at most one edge of G . 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 t...
متن کاملGeneralized Steiner Systems
Generalized Steiner systems GSd t; k; v; g were ®rst introduced by Etzion and used to construct optimal constant-weight codes over an alphabet of size g 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS 2; 3; v; g. However, for block size four there is not much known on GSd 2...
متن کاملReporting intersections among thick objects
Let E be a set of n objects in fixed dimension d. We assume that each element ofE has diameter smaller than D and has volume larger than V . We give a new divide and conquer algorithm that reports all the intersecting pairs in O(n logn + Dd V (n + k)) time and using O(n) space, where k is the number of intersecting pairs. It makes use of simple data structures and primitive operations, which ex...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90054-5