The completion of partial Latin squares
نویسنده
چکیده
In recent times there has been some interest in studying partial latin squares which have no completions or precisely one completion, and which are critical with respect to this property. Such squares are called, respectively, premature partial latin squares and critical sets. There has also been interest in related maximal partial latin squares. This paper will explore the connection between these three structures and review some of the literature in this area. A number of open problems are presented.
منابع مشابه
Completion of Partial Latin Squares
In this thesis, the problem of completing partial latin squares is examined. In particular, the completion problem for three primary classes of partial latin squares is investigated. First, the theorem of Marshall Hall regarding completions of latin rectangles is discussed. Secondly, a proof of Evans’ conjecture is presented, which deals with partial latin squares of order n containing at most ...
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The problem of completing partial latin squares to latin squares of the same order has been studied for many years. For instance, in 1960 Evans [9] conjectured that every partial latin square of order n containing at most n− 1 filled cells is completable to a latin square of order n. This conjecture was shown to be true by Lindner [12] and Smetaniuk [13]. Recently, Bryant and Rodger [6] establi...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 22 شماره
صفحات -
تاریخ انتشار 2000