### Abstract

Given an n × n matrix A = [a_{ij}], a transversal of A is a set of elements, one from each row and one from each column. A transversal is a latin transversal if no two elements are the same. Erdös and Spencer showed that there always exists a latin transversal in any n × n matrix in which no element appears more than s times, for s≤ (n - 1)/16. Here we show that, in fact, the elements of the matrix can be partitioned into n disjoint latin transversals, provided n is a power of 2 and no element appears more than εn times for some fixed ε>0. The assumption that n is a power of 2 can be weakened, but at the moment we are unable to prove the theorem for all values of n.

Original language | English (US) |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Feb 10 1995 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

*57*(1), 1-10. https://doi.org/10.1016/0166-218X(93)E0136-M

**Covering with latin transversals.** / Alon, Noga; Spencer, Joel; Tetali, Prasad.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 57, no. 1, pp. 1-10. https://doi.org/10.1016/0166-218X(93)E0136-M

}

TY - JOUR

T1 - Covering with latin transversals

AU - Alon, Noga

AU - Spencer, Joel

AU - Tetali, Prasad

PY - 1995/2/10

Y1 - 1995/2/10

N2 - Given an n × n matrix A = [aij], a transversal of A is a set of elements, one from each row and one from each column. A transversal is a latin transversal if no two elements are the same. Erdös and Spencer showed that there always exists a latin transversal in any n × n matrix in which no element appears more than s times, for s≤ (n - 1)/16. Here we show that, in fact, the elements of the matrix can be partitioned into n disjoint latin transversals, provided n is a power of 2 and no element appears more than εn times for some fixed ε>0. The assumption that n is a power of 2 can be weakened, but at the moment we are unable to prove the theorem for all values of n.

AB - Given an n × n matrix A = [aij], a transversal of A is a set of elements, one from each row and one from each column. A transversal is a latin transversal if no two elements are the same. Erdös and Spencer showed that there always exists a latin transversal in any n × n matrix in which no element appears more than s times, for s≤ (n - 1)/16. Here we show that, in fact, the elements of the matrix can be partitioned into n disjoint latin transversals, provided n is a power of 2 and no element appears more than εn times for some fixed ε>0. The assumption that n is a power of 2 can be weakened, but at the moment we are unable to prove the theorem for all values of n.

UR - http://www.scopus.com/inward/record.url?scp=58149209442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149209442&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(93)E0136-M

DO - 10.1016/0166-218X(93)E0136-M

M3 - Article

AN - SCOPUS:58149209442

VL - 57

SP - 1

EP - 10

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1

ER -