Families of k-independent sets

Daniel J. Kleitman, Joel Spencer

Research output: Contribution to journalArticle

Abstract

A collection F of sets is k-independent if for any selections A, B of k1 and k2 of its members with k1+k2=k, there are elements in all the members of A and not in the members of B. Bounds on the maximal size of k-independent families exponential in the total number of elements are obtained.

Original languageEnglish (US)
Pages (from-to)255-262
Number of pages8
JournalDiscrete Mathematics
Volume6
Issue number3
DOIs
StatePublished - 1973

Fingerprint

Independent Set
Exponential Family
Family

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Families of k-independent sets. / Kleitman, Daniel J.; Spencer, Joel.

In: Discrete Mathematics, Vol. 6, No. 3, 1973, p. 255-262.

Research output: Contribution to journalArticle

Kleitman, Daniel J. ; Spencer, Joel. / Families of k-independent sets. In: Discrete Mathematics. 1973 ; Vol. 6, No. 3. pp. 255-262.
@article{a5c291a11f6e4ae6a6dce26eb7b4a186,
title = "Families of k-independent sets",
abstract = "A collection F of sets is k-independent if for any selections A, B of k1 and k2 of its members with k1+k2=k, there are elements in all the members of A and not in the members of B. Bounds on the maximal size of k-independent families exponential in the total number of elements are obtained.",
author = "Kleitman, {Daniel J.} and Joel Spencer",
year = "1973",
doi = "10.1016/0012-365X(73)90098-8",
language = "English (US)",
volume = "6",
pages = "255--262",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Families of k-independent sets

AU - Kleitman, Daniel J.

AU - Spencer, Joel

PY - 1973

Y1 - 1973

N2 - A collection F of sets is k-independent if for any selections A, B of k1 and k2 of its members with k1+k2=k, there are elements in all the members of A and not in the members of B. Bounds on the maximal size of k-independent families exponential in the total number of elements are obtained.

AB - A collection F of sets is k-independent if for any selections A, B of k1 and k2 of its members with k1+k2=k, there are elements in all the members of A and not in the members of B. Bounds on the maximal size of k-independent families exponential in the total number of elements are obtained.

UR - http://www.scopus.com/inward/record.url?scp=0000294926&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000294926&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(73)90098-8

DO - 10.1016/0012-365X(73)90098-8

M3 - Article

VL - 6

SP - 255

EP - 262

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -