A Critique of Deng's "P=NP"

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