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Pseudo orthogonal Latin squares

  • Shahab Faruqi EMAIL logo , S. A. Katre and Manisha Garg

Abstract

Two Latin squares A, B of order n are called pseudo orthogonal if for any 1 ≤ i, jn there exists a k, 1 ≤ kn, such that A(i, k) = B(j, k). We prove that the existence of a family of m mutually pseudo orthogonal Latin squares of order n is equivalent to the existence of a family of m mutually orthogonal Latin squares of order n. We also obtain exact values of clique partition numbers of several classes of complete multipartite graphs and of the tensor product of complete graphs.


Note: Originally published in Diskretnaya Matematika (2020) 32, №3, 113–129 (in Russian).



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Acknowledgement

The authors thank Bhaskaracharya Pratishthana (Institute of Mathematics), Pune, for certain facilities and A. Zubkov for his helpful comment regarding computational complexity. The second author thanks support from Lokmanya Tilak Chair, S. P. Pune University, for research facilities.

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Received: 2020-04-16
Published Online: 2021-02-16
Published in Print: 2021-02-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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