### 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) |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Feb 10 1995 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

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