Cycle packing

In the 1960s, Erdi¾?s and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into On cycles and edges. They observed that one can easily get an Onlogn upper bound by repeatedly removing the edges of the longest cycle. We make the first progress on this problem, showing that Onloglogn cycles and edges suffice. We also prove the Erdi¾?s-Gallai conjecture for random graphs and for graphs with linear minimum degree. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 608-626, 2014

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