# Combinatorics and Graph Theory

## 1603 Submissions

[2] **viXra:1603.0218 [pdf]**
*submitted on 2016-03-15 07:27:51*

### Minor of K-Chromatic Graphs, Four Color Theorem and Hadwiger Conjecture

**Authors:** Ali Reza Najar Saligheh

**Comments:** 6 Pages. English and French languages.

First we will prove that Kk (the complete graph with k vertices) is a minor of every graph with chromatic number k. Then we will prove some other statements such as the four color theorem and the Hadwiger conjecture. We will not use computer-assisted proofs.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1603.0041 [pdf]**
*submitted on 2016-03-03 10:06:19*

### On Bipolar Single Valued Neutrosophic Graphs

**Authors:** Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache

**Comments:** 19 Pages. http://www.newtheory.org

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties

**Category:** Combinatorics and Graph Theory