Intersecting Designs

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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[formula]. In fact, this result is a special case of a much more general result, which determines the existence of k distinct Kr-decompositions of Kn which have q elements in common, and all other elements of any two of the decompositions share at most one edge in common.

Original languageEnglish
Pages (from-to)113-125
Number of pages13
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - Jan 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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