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| Év szerint | Hónap szerint | Ugrás a hónaphoz | |||||||
Asaf Ferber (ETH): Finding an oriented Hamilton cycle in a pseudorandom digraph |
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| Abstract. 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 my amazing team from ETH, Zurich: Rajko Nenadov, Andreas Noever, Ueli Peter and Nemanja Skoric. |
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| Hely : Kalmár Intézet, Árpád tér, szemináriumi szoba | ||||
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