When is an incomplete 3× n latin rectangle completable?
نویسندگان
چکیده
We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.
منابع مشابه
A note on the completion of partial latin squares
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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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 33 شماره
صفحات -
تاریخ انتشار 2013