In 1974 Allan Cruse provided necessary and sufficient conditions to extend an $r\times s$ partial latin rectangle consisting of $t$ distinct symbols to a latin square of order $n$. Here we provide some generalizations and consequences of this result. Our results are obtained via an alternative proof of Cruse's theorem.
Transversals in Latin arrays with many distinct symbols
Sufficient conditions for the existence of a path-factor which are related to odd components
Sufficient conditions for graphs to be $k$-connected, maximally connected and super-connected
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