On the minimum number of entries in a pair of maximal orthogonal partial Latin squares

Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı

It is shown that if $F$ denotes the number of filled cells in a superimposed pair of maximal orthogonal partial Latin squares of order $n$, then $F\ge n^2/3$. This resolves a conje…