Finding Regular Subgraphs in Graph Theory

Explore a mathematics seminar presentation that delves into the fascinating world of regular subgraphs and their discovery methods. Learn about the historical progression from Erdős and Sauer's 1975 question through Pyber's 1985 breakthrough to recent developments by Janzer and Sudakov. Understand the comprehensive framework for finding regular subgraphs across all possible r-values, incorporating algebraic techniques from Alon, Friedland and Kalai, recent advances in the sunflower conjecture, and methods for identifying almost-regular subgraphs. Discover a novel random process that efficiently locates nearly regular subgraphs within almost-regular graphs, presented through collaborative research with Debsoumya Chakraborti, Oliver Janzer and Abhishek Methuku. Gain insights into why finding regular subgraphs is valuable, particularly when proving theorems or working with regular graphs.