Packing Tree Factors in Random and Pseudo-random Graphs

For a xed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a xed tree T on t vertices and > 0, the random graph Gn;p, with n a multiple of t, with high probability contains a family of edge-disjoint T -factors covering all but an -fraction of its edges, as long as 4 np log 2 n. Assuming stronger divisibility conditions, the edge probability can be taken down to p > C logn n . A similar packing result is proved also for pseudorandom graphs, dened in terms of their degrees and co-degrees.

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