Please read the statement and intuition about Szemer`edi’s regularity lemma. Problem 1: In the definition of (A, B) as an -regular pair (or -pseudo-random pair), what is the purpose of the requirement that for every subset X ⊆ A and Y ⊆ B, |X| ≥ |A| and |Y | ≥ |B|? Problem 2: Prove that any -regular pair in G is also -regular in G.
