There are several theorems associated with the name König or Kőnig:
Kőnig's theorem (set theory), named after the Hungarian mathematician Gyula Kőnig. Kőnig's theorem (complex analysis), named after the Hungarian mathematician Gyula Kőnig. Kőnig's theorem (graph theory), named after his son Dénes Kőnig. König's theorem (kinetics), named after the German mathematician Samuel König.
See also Kőnig's lemma (also known as Kőnig's infinity lemma), named after Dénes Kőnig