Intersecting Designs

Yair Caro; Raphael Yuster

doi:10.1006/jcta.1999.3039

Intersecting Designs

Yair Caro, Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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[formula]. 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.

Original language	English
Pages (from-to)	113-125
Number of pages	13
Journal	Journal of Combinatorial Theory. Series A
Volume	89
Issue number	1
DOIs	https://doi.org/10.1006/jcta.1999.3039
State	Published - Jan 2000

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1006/jcta.1999.3039

Cite this

@article{f29496c58db94de2a23f4822992fd664,

title = "Intersecting Designs",

abstract = "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.",

author = "Yair Caro and Raphael Yuster",

year = "2000",

month = jan,

doi = "10.1006/jcta.1999.3039",

language = "English",

volume = "89",

pages = "113--125",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Intersecting Designs

AU - Caro, Yair

AU - Yuster, Raphael

PY - 2000/1

Y1 - 2000/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041993723&partnerID=8YFLogxK

U2 - 10.1006/jcta.1999.3039

DO - 10.1006/jcta.1999.3039

M3 - Article

AN - SCOPUS:0041993723

SN - 0097-3165

VL - 89

SP - 113

EP - 125

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -

Intersecting Designs

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this