Packing tree factors in random and pseudo-random graphs

Deepak Bal, Alan Frieze, Michael Krivelevich, Po Shen Loh

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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.

Original languageEnglish
JournalElectronic Journal of Combinatorics
Volume21
Issue number2
Publication statusPublished - 16 Apr 2014

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Keywords

  • Packing
  • Pseudo-random graphs
  • Random graphs
  • Tree factors

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