### 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 language | English (US) |
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Pages (from-to) | 55-61 |

Number of pages | 7 |

Journal | Combinatorica |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1981 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Mathematics

### Cite this

*Combinatorica*,

*1*(1), 55-61. https://doi.org/10.1007/BF02579177

}

*Combinatorica*, vol. 1, no. 1, pp. 55-61. https://doi.org/10.1007/BF02579177

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

Research output: Contribution to journal › Article

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 -