Intersecting Designs

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In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Caro Y. ;&nbsp; Yuster R.

Authors: Caro Y.; Yuster R.

Source: Journal of Combinatorial Theory, Series A, Volume 89, Number 1, January 2000 , pp. 113-125(13)

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Abstract:

We prove the intersection conjecture for designs: For any complete graph K_r there is a finite set of positive integers M(r) such that for every n>n₀(r), if K_n has a K_r-decomposition (namely a 2-(n, r, 1) design exists) then there are two K_r-decompositions of K_n having exactly q copies of K_r in common for every q belonging to the set. In fact, this result is a special case of a much more general result, which determines the existence of k distinct K_r-decompositions of K_n which have q elements in common, and all other elements of any two of the decompositions share at most one edge in common. Copyright 2000 Academic Press.