Critical Sets In Latin Squares Of Order Less Than \(11\)

A critical set \(C\) in a Latin square \(L\) is a partial Latin square which has a unique completion to \(L\) and for which no subset of \(C\) has this property. In this paper, I document known results on the possible sizes of critical sets, and provide a reference list
for the existence of critical sets in Latin squares of order less than or equal to \(10\).
Many of the results in this list are new, and where this is the case, I exhibit a critical set of the given size in the Appendix.