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

Date and Time: Tuesday, September 17, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Miloš Trujić

Rödl-Ruciński theorem for large graphs

A seminal result of Rödl and Ruciński from 1995 states that for every fixed graph H a random graph G(n, p) is w.h.p. such that every 2-colouring of its edges contains a monochromatic copy of H in one of the two colours, provided that p >> n^(-1/m_2(H)), where the value m_2(H) is a certain (natural) density parameter of the graph H. We extend this theorem to all 'large' graphs H with maximum degree three. Namely, there is a b > 0 and a C > 0 for which w.h.p. a random graph G(n, p) is such that every 2-colouring of its edges contains a monochromatic copy of every graph H with b*n vertices and maximum degree at most three, provided that p >= Cn^(-2/5). The value 2/5 in the density p is optimal, which stems from the Rödl-Ruciński theorem. The statement has immediate consequences for the size-Ramsey numbers of large graphs, improving a result of Kohayakawa, Rödl, Schacht, and Szemerédi. This is a joint work with David Conlon and Rajko Nenadov.

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