Set Theory and Logic


Solution to the Traveling Salesman Problem as a Theorem, Unrelated to P, NP

Authors: Colin James III

We evaluate the traveling salesman problem (TSP) to confirm it as a theorem but with multiple solutions for n = 4 cities. The number of solutions here is also given by n = 4. Our results do not relate to P, NP, or NP-hard. Hence the salesman problem as an outstanding mathematical problem of optimization is refuted, and as such becomes a non tautologous fragment of the universal logic VŁ4.

Comments: 1 Page. Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at

Download: PDF

Submission history

[v1] 2019-08-27 18:38:37

Unique-IP document downloads: 19 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus