2015•arXiv (Cornell University)Open access

A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami

Hector A. Cardenas, Chester Holtz, Maria Janczak, Philip R. Meyers, Nathaniel S. Potrepka

Abstract

In this work, we critique two papers, "A Polynomial-Time Solution to the Clique Problem" by Tamta, Pande, and Dhami, and "A Polynomial-Time Algorithm For Solving Clique Problems" by LaPlante. We summarize and analyze both papers, noting that the algorithms presented in both papers are flawed. We conclude that neither author has successfully established that P = NP.

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Key concepts: Clique, Mathematical proof, Clique problem, Polynomial, Mathematics, Time complexity, P versus NP problem, Computer science