Szemerédi's Graph Regularity Lemma
A bounded partition makes most vertex pairs behave regularly with respect to edge density. The energy-increment proof explains why repeated refinements terminate, despite the rapidly growing number of parts.
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Finite Simple Graph · bipartite graph · Extremal Graph Theory
Where to read
Start here: Graph Theory and Additive Combinatorics: Exploring Structure and Randomness (author manuscript)
Yufei Zhao · Book · English · Free full text
§2.1 Szemerédi's Graph Regularity Lemma, Theorem 2.1.9 and its energy-increment proof
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Combinatorics & Graph Theory in the library · Preparation and skip guidance