Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2001-04

September 2001

Clique Facets of the Orthogonal Latin Squares Polytope

G. Appa, D. Magos, I. Mourtos, and J. C. M. Janssen


This paper presents a partial polyhedral characterisation of the Orthogonal Latin Squares (OLS) polytope. First, the dimension of the polytope is derived. Furthermore, three collectively exhaustive classes of cliques of the underlying intersection graph are described. Two of these classes induce facet-defining inequalities of Chvátal rank two, whereas the third one gives rise to the minimum equality system of the polytope. For each class of facets, a separation algorithm of the lowest possible complexity is also presented.

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