# MathSciDoc: An Archive for Mathematician ∫

#### Best Paper Award in Applied Mathematics in 2020

Annals of Mathematics, 190, 949-955, 2019.11
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 result is best possible, and improves a logarithmic lower bound shown by Chung, F\"uredi, 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.
@inproceedings{hao2019induced,
title={Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture},
author={Hao Huang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200512024647968550671},
booktitle={Annals of Mathematics},
volume={190},
pages={949-955},
year={2019},
}

Hao Huang. Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture. 2019. Vol. 190. In Annals of Mathematics. pp.949-955. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200512024647968550671.