Document Type

Article

Publication Date

4-16-2014

Journal / Book Title

The Electronic Journal of Combinatorics

Abstract

For a fixed 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 fixed tree T on t vertices and ε > 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 ε-fraction of its edges, as long as ε4np ≫ log2 n. Assuming stronger divisibility conditions, the edge probability can be taken down to p >. A similar packing result is proved also for pseudo- random graphs, defined in terms of their degrees and co-degrees.

DOI

10.37236/3285

Journal ISSN / Book ISBN

ISSN: 1077-8926

Published Citation

Bal, D., Frieze, A., Krivelevich, M., & Loh, P. S. (2014). Packing Tree Factors in Random and Pseudo-Random Graphs. The Electronic Journal of Combinatorics, P2-8.

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