Complex sentence: Komlós, Sárközy and Szemerédi later proved in the blow-up lemma that the regular pairs in Szemerédi regularity lemma behave like complete bipartite graphs under the correct conditions, allowing for deeper exploration into the nature of embeddings of large sparse graphs into dense graphs.
Split into simpler sentences: Komlós, Sárközy and Szemerédi later proved in the blow-up lemma that the regular pairs in Szemerédi regularity lemma behave like complete bipartite graphs under the correct conditions. The lemma allowed for deeper exploration into the nature of embeddings of large sparse graphs into dense graphs.