An Introduction to Seymour’s Second Neighbourhood Conjecture.

Title of the Talk: T An Introduction to Seymour’s Second Neighbourhood Conjecture.
Speakers: Shiwali
Host Faculty: Dr.Maria Francis
Date: Oct 29, 2025
Time: 02:30pm
Venue: CS LH1

Abstract: Seymour’s Second Neighbourhood Conjecture is a well-known open problem in graph theory. It states that in every finite digraph, there exists a vertex whose number of second neighbours is at least as large as its number of first neighbours. While the conjecture has not been resolved in full, several partial results have been established over the years. The problem has been studied in various settings, leading to interesting progress in many specific cases. In this talk, I will give an overview of the conjecture, discuss key known results.

Bio: Shiwali is a fifth-year Ph.D. student in the Department of Computer Science at IIT Hyderabad, under the supervision of Dr. Rogers Mathew. My research is in graph theory and combinatorics, where I focus on extremal questions and hardness results in conflict-free coloring of graphs and hypergraphs. I also work on the list variant of conflict-free coloring.