ABSTRACT
As a somewhat unexpected application, we shall use the one-factorizations of K6 to prove the uniqueness of the projective plane PG(2, 4).
We first return to the study of ovals in projective planes (see Section 4.1). Recall that any 2-arc in a PG(2, n) has at most n+2 points; those with n+1 and n + 2 points are called type I and type II ovals respectively. We shall define an arc to be maximal if it is not a proper subset of any (larger) arc.
