A Critique of Deng's "P=NP"

Isabel Humphreys; Matthew Iceland; Harry Liuson; Dylan McKellips; Leo Sciortino

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arXiv · 2507.09018

A Critique of Deng's "P=NP"

Isabel Humphreys·Matthew Iceland·Harry Liuson·Dylan McKellips·Leo Sciortino

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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 $\text{P}=\text{NP}$.

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BibTeX RIS

Isabel Humphreys, Matthew Iceland, Harry Liuson, Dylan McKellips, Leo Sciortino. 2025-07-11. A Critique of Deng's "P=NP". https://arxiv.org/abs/2507.09018

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