Combinatorics and Graph Theory

1809 Submissions

[2] viXra:1809.0188 [pdf] submitted on 2018-09-09 10:39:33

The Clique Problem - A Polynomial Time and Non-Heuristic Solution

Authors: John Archie Gillis
Comments: 53 Pages.

The Clique Problem This paper provides a Polynomial Time and Non-Heuristic Solution to the Clique problem. Methods are given to find: 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. 4.Finding cliques of a selected size, particularly largest cliques.
Category: Combinatorics and Graph Theory

[1] viXra:1809.0050 [pdf] submitted on 2018-09-02 10:40:32

The 2n-2 Lines Proof of the n x n Points Puzzle

Authors: Marco Ripà
Comments: 9 Pages.

This paper offers the first proof that the minimal solution of the n x n dots puzzle, for any n≥3, counts 2n-2 lines. Furthermore, a general criterion to solve any n x n grid is given.
Category: Combinatorics and Graph Theory