Set Theory and Logic

2009 Submissions

[2] viXra:2009.0209 [pdf] submitted on 2020-09-30 19:27:22

The Clique Problem with Collaborative Variables (P=NP)

Authors: John Archie Gillis
Comments: 15 Pages.

The present paper provides a novel approach to solving the clique problem(s). The present methods will work for any clique problem, including those which are determined to be NP-Complete. Determining other cliques, such as cliques of a fixed size (k=3, k=4, etc.) is trivial by comparison but will also be described. The author provides a means for greatly reducing the time that it will take a computer (or human) to solve for: 1. Maximum clique (a clique with the largest possible number of vertices), 2. Listing all maximal cliques (cliques that cannot be enlarged), and 3. Solving the decision problem of testing whether a graph contains a clique larger than a given size. To solve the clique problem, the author feels that we must completely discard previous graphing methods and start from scratch with his new and novel strategy.
Category: Set Theory and Logic

[1] viXra:2009.0002 [pdf] submitted on 2020-09-01 08:41:21

Math: An Invention or a Discovery?

Authors: Joseph Palazzo
Comments: 6 Pages.

Math is a process in which both invention and discovery are essential ingredients in its development. But which one comes first?
Category: Set Theory and Logic