On avoiding odd partial Latin squares and \(r\)-multi Latin squares (Q860463)

A partial Latin square \({\mathcal R}\) is avoidable if there exists a Latin square \({\mathcal L}\) such that the entries in corresponding cells are never equal. The authors extend a result of \textit{A. G. Chetwynd} and \textit{S. J. Rhodes} [Discrete Math. 177, 17--32 (1997; Zbl 0898.05008)] and establish that every partial Latin square of odd order at least 7 that contains an empty row (or column) is avoidable. They also prove several results regarding avoidability for partial \(r\)-multi Latin squares.