Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, June 14, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Rajko Nenadov

On a Ramsey-Turán variant of the Hajnal-Szemerédi theorem

The Hajnal-Szemerédi theorem states that every graph G with n vertices and minimum degree at least (r-1)n/r contains a K_r-factor, that is a collection of disjoint copies of the complete graph on r vertices which together cover all the vertices of G, assuming r divides n. The bound on the minimum degree is easily seen to be optimal: take a complete r-partite graph in which one vertex class is of size n/r -1, one n/r + 1 and all other of size n/r. Such a graph has minimum degree (r-1)n/r - 1 and clearly does not contain K_r-factor. One particular feature of this example is that it contains a very large independent set. What happens if we exclude graphs with this property? Does a weaker bound on the minimum degree imply a K_r-factor if we additionally assume that G has sublinear independence number? In this talk I will give an overview of known results, present some new ones and discuss further research directions. Based on a joint work with Yanitsa Pehova (University of Warwick).

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

Previous talks by year:   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