### Abstract

We show for all n is not an element of 1, 2, 4 that there exists a latin square of order n that contains two entries gamma(1) and gamma(2) such that there are some transversals through gamma(1) but they all include gamma(2) as well. We use this result to show that if n > 6 and n is not of the form 2p for a prime p >= 11 then there exists a latin square of order n that possesses an orthogonal mate but is not in any triple of MOLS. Such examples provide pairs of 2-maxMOLS

Original language | English |
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Pages (from-to) | 796 - 807 |

Number of pages | 12 |

Journal | Journal of Combinatorial Theory - Series A |

Volume | 118 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2011 |

## Cite this

Danziger, P., Wanless, I. M., & Webb, B. (2011). Monogamous latin squares.

*Journal of Combinatorial Theory - Series A*,*118*(3), 796 - 807. https://doi.org/10.1016/j.jcta.2010.11.011