Title: Spectral Turan Problems on trees and even cycles
| Speaker: | Dheer Noal |
| Affiliation: | University of Delaware |
| Zoom: | Please contact Sabrina Lato for Zoom link |
Abstract: In this talk, we discuss some recent progress with the spectral analogue of a few Turán problems: Instead of maximizing the number of edges, our objective is to maximize the spectral radius of the adjacency matrices of graphs not containing some subgraphs.
We discuss an overview comparing extremal graphs for both kinds of problems. The asymptotics of the Turán numbers for graphs with chromatic number at least three is given by a celebrated theorem of Erdős, Stone and Simonovits, and a similar result holds for the spectral Turán numbers. However, the asymptotics are not known for several basic bipartite graphs.
We discuss a method that was initially used to obtain spectral Turán results when the forbidden graphs had chromatic number more than two, and has recently been used to find spectral extremal graphs for even cycles and trees.