Geodesic
Pseudo orthogonal Latin squares
Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 113-129

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Two Latin squares $A,B$ of order $n$ are called pseudo orthogonal if for any $1\le i,j\le n$ there exists a $k,1\le k\le n$, 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.
Keywords: Latin squares, clique partition number, intersection number. 
@article{DM_2020_32_3_a8,
     author = {S. Faruqi and S. Katre and M. Garg},
     title = {Pseudo orthogonal {Latin} squares},
     journal = {Diskretnaya Matematika},
     pages = {113--129},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_3_a8/}
}
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S. Faruqi; S. Katre; M. Garg. Pseudo orthogonal Latin squares. Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 113-129. http://geodesic.mathdoc.fr/item/DM_2020_32_3_a8/