A Critique of Deng's "P=NP"
Computational Complexity
2025-07-15 v1
Abstract
In this paper, we critically examine Deng's "P=NP" [Den24]. The paper claims that there is a polynomial-time algorithm that decides 3-coloring for graphs with vertices of degree at most 4, which is known to be an NP-complete problem. Deng presents a semidefinite program with an objective function that is unboundedly negative if the graph is not 3-colorable, and a minimum of 0 if the graph is 3-colorable. Through detailed analysis, we find that Deng conflates subgraphs with induced subgraphs, leading to a critical error which thereby invalidates Deng's proof that .
Cite
@article{arxiv.2507.09018,
title = {A Critique of Deng's "P=NP"},
author = {Isabel Humphreys and Matthew Iceland and Harry Liuson and Dylan McKellips and Leo Sciortino},
journal= {arXiv preprint arXiv:2507.09018},
year = {2025}
}
Comments
10 pages, 4 figures