Abstract
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 $\sqrt{n}$. This is the best possible result, and it 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.
Citation
Hao Huang. "Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture." Ann. of Math. (2) 190 (3) 949 - 955, November 2019. https://doi.org/10.4007/annals.2019.190.3.6
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