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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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Gentle(-er) Introduction to Erdős–Bollobás's solution to Ramsey–Turán Type Problem

I am currently trying to understand the construction of maximal graph which contains no $K_4$ and sub-linear number of independent points in the graph. The original paper On a Ramsey–Turán type proble …
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Gentle(-er) Introduction to Erdős–Bollobás's solution to Ramsey–Turán Type Problem

I found an excellent account of this problem in the thesis of John Lenz: xtremal graph theory: Ramsey-Turán numbers, chromatic thresholds, and minors Lenz, John E.
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