ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 33(1) (2013) 57-69
DOI: 10.7151/dmgt.1648

Dedicated to Mieczysław Borowiecki on his 70th birthday

When Is an Incomplete 3× n Latin Rectangle Completable?

Reinhardt Euler

Université Européenne de Bretagne and Lab-STICC, CNRS, UMR 6285,
Université de Brest, B.P.809,
20 Avenue Le Gorgeu, 29285 Brest Cedex, France

Paweł Oleksik

AGH University of Science and Technology,
Faculty of Geology, Geophysics and Environment Protection,
Department of Geoinformatics and Applied Computer Science,
30-059 Cracow, Poland


We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.

Keywords: incomplete latin rectangle, completability, solution space enumeration, branch-and-bound

2010 Mathematics Subject Classification: 05B15, 05C65.


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Received 24 March 2012
Revised 26 July 2012
Accepted 27 July 2012