Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

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

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Miloš Trujić

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: 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