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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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Is every graph an incomparability graph?
Any incomparability graph is perfect (shown by Dilworth in 1950), so any non-perfect graph will be a counterexample. For an explicit counterexample, choose the cycle on $5$ vertices.