### Abstract

In this paper we show that properly edge-colored graphs G with |V(G)|G)2/3. This result extends (with a weaker error term) the well-known result that a factorization of the complete bipartite graph Kn,_{n} has a rainbow matching of size n-o(n), or equivalently that every Latin square of order n has a partial transversal of size n-o(n) (an asymptotic version of the Ryser-Brualdi conjecture). In this direction we also show that every Latin square of order n has a cycle-free partial transversal of size n-o(n).

Original language | English |
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Pages (from-to) | 96-102 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 327 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 28 2014 |

### Fingerprint

### Keywords

- Partial transversals in Latin squares
- Proper edge colorings
- Rainbow matchings

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*327*(1), 96-102. https://doi.org/10.1016/j.disc.2014.03.010

**Rainbow matchings and cycle-free partial transversals of Latin squares.** / Gyárfás, A.; Sárközy, Gábor N.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 327, no. 1, pp. 96-102. https://doi.org/10.1016/j.disc.2014.03.010

}

TY - JOUR

T1 - Rainbow matchings and cycle-free partial transversals of Latin squares

AU - Gyárfás, A.

AU - Sárközy, Gábor N.

PY - 2014/7/28

Y1 - 2014/7/28

N2 - In this paper we show that properly edge-colored graphs G with |V(G)|G)2/3. This result extends (with a weaker error term) the well-known result that a factorization of the complete bipartite graph Kn,n has a rainbow matching of size n-o(n), or equivalently that every Latin square of order n has a partial transversal of size n-o(n) (an asymptotic version of the Ryser-Brualdi conjecture). In this direction we also show that every Latin square of order n has a cycle-free partial transversal of size n-o(n).

AB - In this paper we show that properly edge-colored graphs G with |V(G)|G)2/3. This result extends (with a weaker error term) the well-known result that a factorization of the complete bipartite graph Kn,n has a rainbow matching of size n-o(n), or equivalently that every Latin square of order n has a partial transversal of size n-o(n) (an asymptotic version of the Ryser-Brualdi conjecture). In this direction we also show that every Latin square of order n has a cycle-free partial transversal of size n-o(n).

KW - Partial transversals in Latin squares

KW - Proper edge colorings

KW - Rainbow matchings

UR - http://www.scopus.com/inward/record.url?scp=84898723892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898723892&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2014.03.010

DO - 10.1016/j.disc.2014.03.010

M3 - Article

VL - 327

SP - 96

EP - 102

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -