منابع مشابه
Intersecting Designs
We prove the intersection conjecture for designs: For any complete graph Kr there is a finite set of positive integers M(r) such that for every n > n0(r), if Kn has a Kr-decomposition (namely a 2-(n, r, 1) design exists) then there are two Kr-decompositions of Kn having exactly q copies of Kr in common for every q belonging to the set {0, 1, . . . , ( n 2 ) / ( r 2 ) }\{ ( n 2 ) / ( r 2 ) −m | ...
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A kite-design of order n is a decomposition of the complete graph Kn into kites. Such systems exist precisely when n ≡ 0, 1 (mod 8). Two kite systems (X,K1) and (X,K2) are said to intersect in m pairwise disjoint blocks if |K1∩K2| = m and all blocks in K1∩K2 are pairwise disjoint. In this paper we determine all the possible values of m such that there are two kite-designs of order n intersectin...
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We investigate l-designs (regular intersecting families) and graphs of diameter 2. The optimal configurations are either projective planes or design-like structures closely related to finite geometries. The new results presented here are corollaries of a recent improvement about uniform hypergraphs with maximal fractional matchings. We propose several open problems.
متن کاملA series of Siamese twin designs intersecting in a BIBD and a PBD
Let p and 2p − 1 be prime powers and p ≡ 3 (mod 4). We describe a construction of a series of Siamese twin designs with Menon parameters (4p, 2p − p, p − p) intersecting in a derived design with parameters (2p − p, p − p, p − p − 1), and a pairwise balanced design PBD(2p − p, {p, p − p}, p − p − 1). When p and 2p − 1 are primes, the derived design and the pairwise balanced design are cyclic. Fu...
متن کاملOn 2-designs Whose Group of Automorphisms Is Transitive on the Ordered Pairs of Intersecting Lines
THEOREM 1. Let G be a permutation group on a finite set S of v points. If a, b are distinct points then the set ab of all points fixed by the stabilizer Gab will be called aline. Assume that (i) G is 2-transitive on the points of S; (ii) the number k of points on the line ab satisfies 2 < k < v; (iii) Gab is transitive on the lines containing a and distinct from ab. Then S provided with the set...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3039