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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Extremal graph theory - many copies of $K_r$ imply a copy of $r$-chromatic $H$
I know that it must be a simple consequence of the Kővári–Sós–Turán (and Erdős–Stone) theorem, but I am struggling to formulate a proof: Let $H$ be a fixed-size $r$-chromatic graph. Then there exists …