[Solved] CSDS455 Homework 15-Szemer`edi’s regularity lemma

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 and ?

Problem 2: Prove that any -regular pair in G is also -regular in G.