# 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