标题： 对邓的“P=NP”的批评 显示英文标题

标题： A Critique of Deng's "P=NP"

摘要： 在本文中，我们对邓的“P=NP”[Den24]进行了批判性检查。 该论文声称存在一个多项式时间算法，可以判断顶点度数最多为4的图的3-coloring，这是一个已知的NP完全问题。 邓提出一个半定规划，其目标函数如果图不可3-coloring，则无界负，如果图可3-coloring，则最小值为0。 通过详细分析，我们发现邓将子图与诱导子图混淆，导致一个关键错误，从而使得邓证明$\text{P}=\text{NP}$的证明无效。 显示英文摘要

摘要： 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 $\text{P}=\text{NP}$.