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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, March 24, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Matthew Kwan

Cycles and matchings in randomly perturbed digraphs and hypergraphs

We consider several situations where "typical" structures have certain spanning substructures (in particular, Hamilton cycles), but where worst-case extremal examples do not. In these situations we show that the extremal examples are "fragile" in that after a modest random perturbation our desired substructures will typically appear.

Our first theorem is that adding linearly many random edges to a dense k-uniform hypergraph typically ensures the existence of a perfect matching or a loose Hamilton cycle. We outline the proof of this theorem, which involves a nonstandard application of Szemeredi's regularity lemma to "beat the union bound"; this might be of independent interest. Our next theorem is that digraphs with certain strong expansion properties are pancyclic. This implies that adding a linear number of random edges typically makes a dense digraph pancyclic. Our final theorem is that perturbing a certain (minimum-degree-dependent) number of random edges in a tournament typically ensures the existence of multiple edge-disjoint Hamilton cycles. All our results are tight.

This is joint work with Michael Krivelevich and Benny Sudakov.

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

Previous talks by year:   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