#### Title

Packing Tree Factors in Random and Pseudo-Random Graphs

#### Document Type

Article

#### Publication Date

4-16-2014

#### 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.

#### MSU Digital Commons Citation

Bal, Deepak; Frieze, Alan; Krivelevich, Michael; and Loh, Po Shen, "Packing Tree Factors in Random and Pseudo-Random Graphs" (2014). *Department of Mathematics Facuty Scholarship and Creative Works*. 135.

https://digitalcommons.montclair.edu/mathsci-facpubs/135