DisCoMath Seminar: The Colin de Verdière Number of a Graph
Discrete & Computational Math Seminar (DisCoMath)
The Colin de Verdière Number of a Graph
Dr. Brendan Rooney
Assistant Professor
School of Mathematical Sciences, RIT
Abstract:
This talk is the first in a series of two talks on "strong" matrix conditions. In this talk we define the Colin de Verdière graph invariant, and show that it is a minor monotone parameter. The Colin de Verdière number of graph G is the maximum multiplicity of 0 as an eigenvalue over matrices compatible with the adjacency matrix of G. In order for M to be compatible with G it must (among other things) satisfy the Strong Arnold Hypothesis. Our focus will be on this property, how it can be interpreted, and how it is applied. We will also discuss the characterization of planar graphs by their Colin de Verdière number. Our discussion follows van der Holst, Lovász, and Schrijver (The Colin de Verdière graph parameter, 1997).
Speaker Bio:
Dr. Rooney is an Assistant Professor in the School of Mathematical Sciences at RIT. He completed his Ph.D. in Combinatorics and Optimization at the University of Waterloo, Ontario, Canada. Prior to joining RIT, he was a Visiting Assistant Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science and Technology (KAIST) for three years. Dr. Rooney’s research interests include Graph Theory, Combinatorics and Combinatorial Optimization.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.
Event Snapshot
When and Where
Who
Open to the Public
Interpreter Requested?
No