## Introduction

Brown, blue, lightgreen, darkgreen, yellow. If you don't know anything about het Behzad-Vizing conjecture, you know that this site uses a lot of colours. In any case, that's a good start, because the conjecture is about colours. Now you know something about the Behzad-Vizing conjecture.

### Behzad-Vizing Conjecture

If we denote the maximum degree of a vertex in a simple graph*G*by

*Δ*(

*G*) and the total chromatic number of

*G*by

*χ"*(

*G*), then:

*χ"*(

*G*)=

*Δ*(

*G*)+1 or

*χ"*(

*G*)=

*Δ*(

*G*)+2.

This conjecture is more well known as Behzad's Conjecture. A. Soifer showed in paragraph 16.2 of his book that V. Vizing was the first person who formulated the conjecture. However, M. Behzad was the first person who, after formulating the same result independently, publicated the conjecture. That's why I follow Soifer's advice to mention both authors.