Disjoint finite partial steiner triple systems can be embedded in disjoint finite steiner triple systems
نویسندگان
چکیده
منابع مشابه
Constructions of Disjoint Steiner Triple Systems
Let D*(v) denote the maximum number of pairwise disjoint and isomorphic Steiner triple systems of order v. The main result of this paper is a lower bound for D*(v), namely D*(6r+3)^ 4t—1 or 4/+1 according as 2/+1 is or is not divisible by 3, and D*(6f+l)^?/2 or t according as t is even or odd. Some other related problems are studied or proposed for study.
متن کاملA Construction of Disjoint Steiner Triple Systems
We show that there are at least 4t + 2 mutually disjoint, isomorphic Steiner triple systems on 6t + 3 points, if t ;?: 4. MiS Subject Classification: OSBOS
متن کاملSteiner Triple Systems Intersecting in Pairwise Disjoint Blocks
Two Steiner triple systems (X,A) and (X,B) are said to intersect in m pairwise disjoint blocks if |A ∩ B| = m and all blocks in A ∩ B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m pairwise disjoint blocks.
متن کاملOn Large Sets of Disjoint Steiner Triple Systems II
A Steiner system S(t, k, V) is a pair (S, /3), where S is a v-set and p is a collection of k-subsets of S called hocks, such that a t-subset of S occurs in exactly one block of p. In particular, an S(2, 3, V) is called a Steiner triple system of order v (briefly STS(v)). It is well known that there is an STS(v) if and only if v E 1 or 3 (mod 6). Two STSs, (S, /3,) and (S, &), are said to be dis...
متن کاملEmbedding Partial Steiner Triple Systems
We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missing-edge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple system of order 2n +1, provided that 2w +1 is admissible. We also prove that if there is a partial Stei...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1975
ISSN: 0097-3165
DOI: 10.1016/0097-3165(75)90073-4