Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture
Combinatorics
2019-09-02 v2 Computational Complexity
Abstract
In this paper, we show that every -vertex induced subgraph of the -dimensional cube graph has maximum degree at least . 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.
Keywords
Cite
@article{arxiv.1907.00847,
title = {Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture},
author = {Hao Huang},
journal= {arXiv preprint arXiv:1907.00847},
year = {2019}
}