Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture

07/01/2019
by   Hao Huang, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/11/2019

On the Resolution of the Sensitivity Conjecture

The Sensitivity Conjecture is a long-standing problem in theoretical com...
research
04/18/2020

Maximal degrees in subgraphs of Kneser graphs

In this paper, we study the maximum degree in non-empty induced subgraph...
research
09/01/2020

On sensitivity in bipartite Cayley graphs

Huang proved that every set of more than half the vertices of the d-dime...
research
01/21/2021

On Separation between the Degree of a Boolean Function and the Block Sensitivity

In this paper we study the separation between two complexity measures: t...
research
12/04/2017

An Upper Bound on the GKS Game via Max Bipartite Matching

The sensitivity conjecture is a longstanding conjecture concerning the r...
research
08/17/2019

Majorana fermions and the Sensitivity Conjecture

Recently, Hao Huang proved the Sensitivity Conjecture, an important resu...
research
08/30/2018

Sensitivity, Affine Transforms and Quantum Communication Complexity

We study the Boolean function parameters sensitivity (s), block sensiti...

Please sign up or login with your details

Forgot password? Click here to reset