A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-
empty cells, and whose corresponding rows and columns contain the same sets of symbols …

Symmetries of a partial Latin square are primarily determined by its autotopism group.
Analogously to the case of Latin squares, given an isotopism Θ, the cardinality of the set …

We discuss the problem of finding critical sets in graphs, a concept which has appeared in a
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …

A critical set in an $ n\times n $ Latin square is a minimal set of entries that uniquely
identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979 …

Completing Latin squares: Critical sets II Page 1 Completing Latin Squares: Critical Sets II Peter
Horak,1 Italo J. Dejter2 1University of Washington, Tacoma, Tacoma, WA 98402-3100, E-mail …

Suppose that L is a latin square of order m and P⊑ L is a partial latin square. If L is the only
latin square of order m which contains P, and no proper subset of P has this property, then P …

If is a partially filled‐in (0, 1)‐matrix with a unique completion to a (0, 1)‐matrix (with
prescribed row and column sums), then we say that is a defining set for. A critical set is a …

Latin trades are closely related to the problem of critical sets in Latin squares. We denote the
cardinality of the smallest critical set in any Latin square of order n by scs (n). A …

If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with
prescribed row and column sums), we say that D is a defining set for M. Let A 2 m, m be the …

We discuss the problem of finding critical sets in graphs, a concept which has appeared in a
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …