# Category: Lemmas in graph theory

Kőnig's lemma
Kőnig's lemma or Kőnig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. It gives a sufficient condition for an infinite graph to h
Szemerédi regularity lemma
Szemerédi's regularity lemma is one of the most powerful tools in extremal graph theory, particularly in the study of large dense graphs. It states that the vertices of every large enough graph can be
Expander mixing lemma
The expander mixing lemma intuitively states that the edges of certain -regular graphs are evenly distributed throughout the graph. In particular, the number of edges between two vertex subsets and is
Blow-up lemma
The blow-up lemma, proved by János Komlós, Gábor N. Sárközy, and Endre Szemerédi in 1997, is an important result in extremal graph theory, particularly within the context of the regularity method. It
Handshaking lemma
In graph theory, a branch of mathematics, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. In more collo