Decomposing large graphs with small graphs of high density

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It is shown that for every positive integer h, and for every ε > 0, there are graphs H = (VH, EH) with at least h vertices and with density at least 0.5 - ε with the following property: If G = (VG, EG) is any graph with minimum degree at least |VG|/2 (1 + o(1)) and \EH| divides \EG|, then G has an H-decomposition. This result extends the results of [R. M. Wilson, Cong Numer XV (1925), 647-659] [T. Gustavsson, Ph.D. Thesis, U. Stockholm, 1991] [R. Yuster, Random Struc Algorith, 12 (1998), 237-251].

Original languageEnglish
Pages (from-to)27-40
Number of pages14
JournalJournal of Graph Theory
Issue number1
StatePublished - Sep 1999


  • Decomposition
  • Dense graphs

ASJC Scopus subject areas

  • Geometry and Topology


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