Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, March 22, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matthew Kwan

Induced subgraphs of Ramsey graphs

An n-vertex graph is called C-Ramsey if it has no clique or independent set of size C log n. We discuss two results showing that all Ramsey graphs must obey certain "richness" properties characteristic of random graphs. First, resolving a conjecture of Narayanan, Sahasrabudhe and Tomon, motivated by an old problem of Erd\H{o}s and McKay, we prove that every C-Ramsey graph has $\Omega(n^2)$ induced subgraphs with different numbers of edges. Second, resolving a conjecture of Erd\H{o}s, Faudree and S\'{o}s, we prove that every C-Ramsey graph has $\Omega(n^{5/2})$ induced subgraphs, no two of which have the same numbers of vertices and edges. This is joint work with Benny Sudakov.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2025  2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login