### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

MAY 5, 2017

**Speaker: **
Carolyn Chun, United States Naval Academy

**Title: ***
Inductive tools for graphs (and matroids)
*

**Abstract:**
In this talk, we consider inductive tools for graphs (and matroids) that preserve a kind of robustness, called connectivity. In 1966, Tutte proved that every 3-connected graph (or matroid) other than a wheel (or whirl) has a single-edge deletion or contraction that is 3-connected. Seymour extended this result in 1980 to show that, in addition to preserving 3-connectivity, we can preserve a given substructure, namely a 3-connected minor. We present the long-running project joint between the speaker, James Oxley, and Dillon Mayhew to obtain such results for graphs (and matroids) that are internally 4-connected.

**Time:** Friday, May 5, 2017, 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