A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami
Hector A. Cardenas, Chester Holtz, Maria Janczak, Philip Meyers and, Nathaniel S. Potrepka
TL;DR
This paper critically examines and refutes two claimed polynomial-time solutions to the clique problem, demonstrating that their algorithms are flawed and that they do not prove P = NP.
Contribution
It provides a detailed critique showing the flaws in the proposed algorithms, clarifying that the P=NP question remains unresolved.
Findings
The algorithms in both papers are flawed.
Neither paper successfully proves P=NP.
The critique clarifies misconceptions in the original claims.
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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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Advanced Combinatorial Mathematics