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Generalized Latin rectangles I: Construction and decomposition

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
31
Issue
2
Identifiers
DOI: 10.1016/0012-365x(80)90030-8

Abstract

Abstract A ( p, q, x)-latin rectangle is a rectangular matrix with x symbols in each cell such that each symbol occurs at most p times in each row and at most q times in each column. We exploit the close correspondence between ( p, q, x)-latin rectangles and equitable edge-colourings of certain graphs. This paper contains results on existence and various forms of decomposition of such rectangles. In a sequel paper embedding is considered.

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