On the origins of Dénes König's infinity lemma
In one of its final versions (1927) the lemma reads: If every point of a connected infinite graph has only finitely many edges going to it, then the graph contains an infinite path. In different guises the lemma appeared repeatedly since D. König's constructivist phase around 1914 when it was used in proofs concerned with the Bernstein theorem of set theory and related subjects. D. König was inspired by work of his father Julius König. The interplay of graph theory and set theory in the work of D. König and the emergence of the lemma are described in detail.
scientific article; zbMATH DE number 1057317
scientific article