# The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras

## TL;DR

This paper presents a new proof of the Sensitivity Conjecture using Clifford algebras, showing that large induced subgraphs of hypercubes have high maximum degree, and extends the result to weighted cases.

## Contribution

It introduces a novel Clifford algebra-based approach to prove the Sensitivity Conjecture and provides a weighted version of the theorem.

## Key findings

- Induced subgraphs with over half the vertices have maximum degree at least √n
- The proof employs Clifford algebras in a natural way
- A weighted version of the main result is established

## Abstract

We give another version of Huang's proof that an induced subgraph of the n-dimensional cube graph containing over half the vertices has maximal degree at least $\sqrt{n}$, which implies the Sensitivity Conjecture. This argument uses Clifford algebras of positive definite signature in a natural way. We also prove a weighted version of the result.