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Study of graphs satisfying a property that are maximal or minimal with respect to some parameter. A classic example is Turán's Theorem, which exactly characterizes the densest graphs on $n$ vertices without a $K_t$ subgraph.

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Intersection property of Szemerédi's regularity condition

We adopt common notations in the study of Szemerédi's regularity lemma and only focus on simple graph $G(V,E)$. For any two disjoint vertex sets $A,B\subset V$, we say the pair $(A,B)$ is $\varepsilon …