### Abstract

This paper surveys some results of the following type: "If a linear program and some derived programs have integral solutions, so does its dual." Several well-known minimax theorems in combinatorics can be derived from such general principles. Similar principles can be proved if integrality is replaced by a condition of the least common denominator of the entries of a solution. An analogy between Tutte's 1-factor-theorem and the Lucchesi-Younger Theorem on disjoint directed cuts is pointed out.

Original language | English |
---|---|

Pages (from-to) | 363-374 |

Number of pages | 12 |

Journal | Annals of Discrete Mathematics |

Volume | 1 |

Issue number | C |

DOIs | |

Publication status | Published - 1977 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

**Certain Duality Principles in Integer Programming.** / Lovász, L.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 1, no. C, pp. 363-374. https://doi.org/10.1016/S0167-5060(08)70744-1

}

TY - JOUR

T1 - Certain Duality Principles in Integer Programming

AU - Lovász, L.

PY - 1977

Y1 - 1977

N2 - This paper surveys some results of the following type: "If a linear program and some derived programs have integral solutions, so does its dual." Several well-known minimax theorems in combinatorics can be derived from such general principles. Similar principles can be proved if integrality is replaced by a condition of the least common denominator of the entries of a solution. An analogy between Tutte's 1-factor-theorem and the Lucchesi-Younger Theorem on disjoint directed cuts is pointed out.

AB - This paper surveys some results of the following type: "If a linear program and some derived programs have integral solutions, so does its dual." Several well-known minimax theorems in combinatorics can be derived from such general principles. Similar principles can be proved if integrality is replaced by a condition of the least common denominator of the entries of a solution. An analogy between Tutte's 1-factor-theorem and the Lucchesi-Younger Theorem on disjoint directed cuts is pointed out.

UR - http://www.scopus.com/inward/record.url?scp=24244435640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24244435640&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70744-1

DO - 10.1016/S0167-5060(08)70744-1

M3 - Article

AN - SCOPUS:24244435640

VL - 1

SP - 363

EP - 374

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -