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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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Number of triangle-free graphs with prescribed number of edges
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Let $f(n, e)$ be the number of triangle-free graphs on $n$ vertices and $e$ edges. From empirical evidence, I am motivated …