### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

MARCH 9, 2018

Brian Cloteaux, NIST
**Speaker: **

**Title: ***
Degree Sequences with Forced Edges
*

**Abstract: **
For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. These edges have applications in areas such as random graph generation based on a given degree sequence and degree sequence packing. In this talk, we examine some of structural implications for graphs whose degree sequences contain either forced or forbidden edges. Among the things we will see, we see some tools to reason about degree sequence containing forced or forbidden edges and how these edges affect the diameter and connectivity for the realizations of these sequences.

**Time:** Friday, March 9, 2018, 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