Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, December 12, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: David Conlon (University of Oxford)

Cycle Packing

In the 1960s, Erdos and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into O(n) cycles and edges. They observed that one can easily get an O(n log n) upper bound by repeatedly removing the edges of the longest cycle. We make the first progress on this problem, showing that O(n log log n) cycles and edges suffice. We also prove the Erdos-Gallai conjecture for random graphs and for graphs with linear minimum degree.

This is joint work with Jacob Fox and Benny Sudakov.

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