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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

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

**Duration**: 30 minutes

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

**Speaker**: Nemanja Skoric

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.

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