Asymptotically optimal Kk-packing of dense graphs via fractional Kk-decompositions

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Let H be a fixed graph. A fractional H-decomposition of a graph G is an assignment of nonnegative real weights to the copies of H in G such that for each e ∈ E (G), the sum of the weights of copies of H containing e is precisely one. An H-packing of a graph G is a set of edge disjoint copies of H in G. The following results are proved. For every fixed k > 2, every graph with n vertices and minimum degree at least n (1 - 1/9k10) + o (n) has a fractional Kk -decomposition and has a Kk-packing which covers all but o (n2) edges.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Combinatorial Theory. Series B
Issue number1
StatePublished - Sep 2005


  • Decomposition
  • Fractional
  • Packing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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