Latin squares with prescribed diagonals

A. J. W. Hilton, C. A. Rodger
1982 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
1. Introduction. An incomplete latin rectangle on t symbols a h . . . , : E(G) -> C, where E(G) is the edge set of G and C is a set of w colours, such that (ei) J* 0(^2) whenever e h e 2 £ £(G) and e x and £ 2 have a common vertex. If G contains 2/ vertices, then a partial matching is a set M of at most / edges such that no two edges of M have a common vertex. If \M\ = t then ikf is a (complete) matching. The following result was proved by G. J. Chang [5] usingabelian groups.
doi:10.4153/cjm-1982-087-7 fatcat:rf427jro6bdq3lzdwn23ay3abu