Integer and Fractional Packings in Dense Graphs

Let be any fixed graph. For a graph G we define to be the maximum size of a set of pairwise edge-disjoint copies of in G. We say a function from the set of copies of in G to [0, 1] is a fractional -packing of G if for every edge e of G. Then is defined to be the maximum value of over all fractional -packings of G. We show that for all graphs G.

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Received July 27, 1998 / Revised December 3, 1999

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Haxell, P., Rödl, V. Integer and Fractional Packings in Dense Graphs. Combinatorica 21, 13–38 (2001).

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  • AMS Subject Classification (2000) Classes:  05C70, 05C85