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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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How to prove a random d-regular graph is an expander with prob >= 0.5?
How to prove a random $d$-regular graph is an expander with prob $\ge 0.5$?
Context: Many resources, like
http://math.mit.edu/~fox/MAT307-lecture22.pdf
state the theorem in the general case, but then …