### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

APRIL 3, 2015

**Speaker: **
Dan Cranston, Virginia Commonwealth University

**Title: ***
Planar graphs are 9/2-colorable and have big independent sets
*

**Abstract:**
For nearly a century, one of the major open questions in graph theory
was the Four Color Conjecture: Every planar graph can be properly
colored with four colors. In 1976, this conjecture was resolved (in
the affirmative) by Appel and Haken. Their result is called the 4
Color Theorem. Unfortunately, their proof (as well as later proofs of
this theorem) relies heavily on computers. In contrast, the 5 Color
Theorem is easy to prove. In this talk we look at a $\frac92$ Color
Theorem, which we can prove by hand.

This is joint work with Landon Rabern.

**Time:** Friday, April 3, 2015, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491