Birkhoff's theorem states:

The set of $n \times n$ doubly stochastic matrices is a convex set whose extreme points are the permutation matrices

This theorem seems to be commonly attributed to Birkhoff (perhaps also von Neumann). But I recall listening to a talk by Harold Kuhn, where he said that this theorem should actually be attributed to some $P$ where $P \in \{$Jacobi, Dénes Kőnig, Jenő Egerváry, Somebody else?$\}$.

Question: Does anybody know whom Kuhn might have meant, and to whom this theorem should really be attributed?

I would be very happy to learn the connection (also, yes, am embarrassed that despite listening carefully during the talk, I have still forgotten!)