## 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: Thursday, September 18, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Dániel Korándi

## Decomposing random graphs into few cycles and edges

Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on $n$ vertices can be decomposed into $O(n)$ cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random graph $G(n,p)$ with probability approaching 1. In this talk we present the following, asymptotically tight, result: For most edge probabilities, $G(n,p)$ can be decomposed into a union of $\frac{n}{4}+\frac{np}{2}+o(n)$ cycles and edges whp.

Joint work with Michael Krivelevich and Benny Sudakov.

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