Pigeonhole Principle and the Probabilistic Method

Abstract

As a story, this means that at a party with n persons, there exist two persons who know the same number of people at the party. Proof. For any graph on n vertices, the degrees are integers between 0 and n − 1. Therefore, the only way all degrees could be different is that there is exactly one vertex of each possible degree. In particular, there is a vertex… (More)

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Cite this paper

@inproceedings{Goemans2015PigeonholePA, title={Pigeonhole Principle and the Probabilistic Method}, author={Michel X. Goemans}, year={2015} }