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

Date and Time: Tuesday, May 27, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nemanja Skoric

Finding an oriented Hamilton cycle in a pseudorandom digraph

Many classic theorems in graph theory can be stated as follows: given a graph G which possesses a graph property P, what is the minimal number of edges (perhaps under some natural restrictions) that one can delete from G such that the obtained graph will no longer satisfy P? Two examples for the case G=Kn are Turan's theorem which solves this problem for the property "containing a clique on k vertices", and Dirac's theorem which states that one can destroy Hamiltonicity without deleting more than n/2 edges touching each vertex. Sudakov and Vu initiated the systematic study of these problems, and since then this field has attracted substantial research interest. Recently, Hefetz, Steger and Sudakov showed that in a typical random directed graph (that is, a graph obtained by tossing a coin with probability p to keep each possible arc (u,v)), one cannot destroy Hamiltonicity (here we mean an oriented Hamilton cycle) by deleting at most (1/2-epsilon)np outedges and at most (1/2-epsilon)np in edges touching each vertex, for p=log n/sqrt{n}. In this talk we will see a simple proof which substantially improves this result to p=polylog n/ n (and is also tight up to a polylog factor).

The result is a joint work with Asaf Ferber, Rajko Nenadov, Andreas Noever and Ueli Peter.

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