A new bound on the size of the largest critical set in a Latin square

Details A new bound on the size of the largest critical set in a Latin square A new bound on the size of the largest critical set in a Latin square

2001-07-23

arxiv.org/abs/math/0107159v1

Discrete Math. 267 (2003) 13-21

Mathematics

Combinatorics

10 pages, LaTeX

Scientific paper

A critical set in an n x n array is a set C of given entries, such that there
exists a unique extension of C to an n x n Latin square and no proper subset of
C has this property. The cardinality of the largest critical set in any Latin
square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that
lcs(n) <= n^2 - n. Here we show that lcs(n) <= n^2-3n+3.

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