a nice probabilistic argument by Alon

These days I am reading “Probabilistic Methods for Algorithmic Discrete Mathematics.” Alon‘s probabilistic proofs are usually beautiful. This one (Theorem 6.1) that I saw today was not an exception. It is really simple to understand, but also very elegant. I can’t help admiring it. It is brilliant. That’s the reason that I like the probabilistic method: because it is full of beautiful proofs. I wish I could write a similar proof someday.

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