Short proof of a theorem of Rado on graphs
Barry Foster · Proceedings of the American Mathematical Society · 1964
Berge's proof [1, p. 18] of Rado's theorem, a special case of the lemma in [2, p. 337], suffers from inaccuracies. In this note the result is derived from the following lemma of Konig [1, p. 17]. If (A1, A2, * * ) is a sequence of nonempty, pairwise disjoint finite sets and < is any relation between elements of consecutive sets such that for all x EA., an element x.-i E A.-, exists with x.-1 < x., then a sequence (a,, a2, *) exists with a.EGA., for all n, such that a,<a2< ... <an< -