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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, May 16, 2019, 12:15 pm

**Duration**: 30 minutes

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

**Speaker**: Erik Jahn

A theorem by Brandt, Chen, Gould, Faudree and Lesniak states that if a graph G on n > 4k vertices has minimum degree at least n/2 then G contains a 2-factor consisting of exactly k cycles. This is quickly seen to be tight in terms of the bound on the minimum degree. However, if one assumes in addition that G is Hamiltonian it has been conjectured that the bound on the minimum degree may be relaxed. This was indeed shown to be true by Sarközy and after a series of improvements the best known result, due to DeBiasio, Ferrara and Morris, established that a minimum degree of (2/5 + o(1))n suffices. We present a major improvement of this result showing that the required minimum degree for large Hamiltonian graphs to have a 2-factor consisting of a fixed number of cycles is sublinear in n. This is joint work with M. Bucic, A. Pokrovskiy and B. Sudakov.

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