Independence numbers of graphs and generators of ideals

Shuo Yen Robert Li, Wen-ching Winnie Li

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

This article investigates the generators of certain homogeneous ideals which are associated with graphs with bounded independence numbers. These ideals first appeared in the theory of t-designs. The main theorem suggests a new approach to the Clique Problem which is NP-complete. This theorem has a more general form in commutative algebra dealing with ideals associated with unions of linear varieties. This general theorem is stated in the article; a corollary to it generalizes Turán's theorem on the maximum graphs with a prescribed clique number.

Original languageEnglish (US)
Pages (from-to)55-61
Number of pages7
JournalCombinatorica
Volume1
Issue number1
DOIs
StatePublished - Mar 1 1981

Fingerprint

Independence number
Algebra
Generator
Graph in graph theory
Theorem
T-designs
Clique number
Commutative Algebra
Clique
Corollary
Union
NP-complete problem
Generalise

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Cite this

Li, Shuo Yen Robert ; Li, Wen-ching Winnie. / Independence numbers of graphs and generators of ideals. In: Combinatorica. 1981 ; Vol. 1, No. 1. pp. 55-61.
@article{75e738f8001340daa7205bba7e53484d,
title = "Independence numbers of graphs and generators of ideals",
abstract = "This article investigates the generators of certain homogeneous ideals which are associated with graphs with bounded independence numbers. These ideals first appeared in the theory of t-designs. The main theorem suggests a new approach to the Clique Problem which is NP-complete. This theorem has a more general form in commutative algebra dealing with ideals associated with unions of linear varieties. This general theorem is stated in the article; a corollary to it generalizes Tur{\'a}n's theorem on the maximum graphs with a prescribed clique number.",
author = "Li, {Shuo Yen Robert} and Li, {Wen-ching Winnie}",
year = "1981",
month = "3",
day = "1",
doi = "10.1007/BF02579177",
language = "English (US)",
volume = "1",
pages = "55--61",
journal = "Combinatorica",
issn = "0209-9683",
publisher = "Janos Bolyai Mathematical Society",
number = "1",

}

Independence numbers of graphs and generators of ideals. / Li, Shuo Yen Robert; Li, Wen-ching Winnie.

In: Combinatorica, Vol. 1, No. 1, 01.03.1981, p. 55-61.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Independence numbers of graphs and generators of ideals

AU - Li, Shuo Yen Robert

AU - Li, Wen-ching Winnie

PY - 1981/3/1

Y1 - 1981/3/1

N2 - This article investigates the generators of certain homogeneous ideals which are associated with graphs with bounded independence numbers. These ideals first appeared in the theory of t-designs. The main theorem suggests a new approach to the Clique Problem which is NP-complete. This theorem has a more general form in commutative algebra dealing with ideals associated with unions of linear varieties. This general theorem is stated in the article; a corollary to it generalizes Turán's theorem on the maximum graphs with a prescribed clique number.

AB - This article investigates the generators of certain homogeneous ideals which are associated with graphs with bounded independence numbers. These ideals first appeared in the theory of t-designs. The main theorem suggests a new approach to the Clique Problem which is NP-complete. This theorem has a more general form in commutative algebra dealing with ideals associated with unions of linear varieties. This general theorem is stated in the article; a corollary to it generalizes Turán's theorem on the maximum graphs with a prescribed clique number.

UR - http://www.scopus.com/inward/record.url?scp=51249180619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249180619&partnerID=8YFLogxK

U2 - 10.1007/BF02579177

DO - 10.1007/BF02579177

M3 - Article

AN - SCOPUS:51249180619

VL - 1

SP - 55

EP - 61

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -