On a class of completable partial edge-colourings (Q1186316)

The problem investigated is the completion problem for partial edge-colourings: given a partial edge-colouring of \(K_{2n-1}\) (of \(K_{2n}\), respectively) with at most \(2n-1\) colours, can it be completed to a minimal edge-colouring of \(K_{2n-1}\) (of \(K_{2n}\), respectively)? In terms of quasigroups, the problem is: given a partial commutative quasigroup of order \(n\), can it be completed to a commutative quasigroup of order \(n\)? The author gives a sufficient condition for a class of partial edge-colourings with a ``large'' number of coloured edges.