Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture
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In this paper, we show that every (2^n-1+1)-vertex induced subgraph of the n-dimensional cube graph has maximum degree at least √(n). This result is best possible, and improves a logarithmic lower bound shown by Chung, Füredi, Graham and Seymour in 1988. As a direct consequence, we prove that the sensitivity and degree of a boolean function are polynomially related, solving an outstanding foundational problem in theoretical computer science, the Sensitivity Conjecture of Nisan and Szegedy.
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