Discrete Applied Mathematics Seminar by Dheer Desai: Spectral Turan Problems on trees and even cycles

Speaker: Dheer Desai, University of Wyoming

Title: Spectral Turán Problems on Trees and Even Cycles

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 forbidden subgraph(s).
We will overview some known results and compare extremal graphs for both kinds of problems. A celebrated theorem of Erdös, Stone and Simonovits gives the asymptotics of the Turán numbers for forbidden graphs with chromatic number more than 2. A similar result also holds for the spectral Turán numbers. In contrast, the asymptotics are not known for several basic bipartite graphs. 

We will discuss a recursive 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.

Please contact the seminar organizers, Samantha Dahlberg (sdahlberg@iit.edu) and Hemanshu Kaul (kaul@iitt.edu), for online joining info.

 

Discrete Applied Math Seminar

Request Zoom link