[CITATION][C] Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven
P Adams, A Khodkar - Ars Combinatoria, 2001 - espace.library.uq.edu.au
A critical set in a latin square of order n is a set of entries in a latin square which can be
embedded in precisely one latin square of order n. Also, if any element of the critical set is
deleted, the remaining set can be embedded in more than one latin square of order n. In this
paper we find smallest weak and smallest totally weak critical sets for all the latin squares of
orders six and seven. Moreover, we computationally prove that there is no (totally) weak
critical set in the back circulant latin square of order five and we find a totally weak critical set …
embedded in precisely one latin square of order n. Also, if any element of the critical set is
deleted, the remaining set can be embedded in more than one latin square of order n. In this
paper we find smallest weak and smallest totally weak critical sets for all the latin squares of
orders six and seven. Moreover, we computationally prove that there is no (totally) weak
critical set in the back circulant latin square of order five and we find a totally weak critical set …
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