Edge-disjoint induced subgraphs with given minimum degree

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Abstract

Let h be a given positive integer. For a graph with n vertices and m edges, what is the maximum number of pairwise edge-disjoint induced subgraphs, each having minimum degree at least h? There are examples for which this number is O(m2=n2). We prove that this bound is achievable for all graphs with polynomially many edges. For all ε> 0, if m > n1+ε, then there are always Ω(m2=n2) pairwise edge-disjoint induced subgraphs, each having minimum degree at least h. Furthermore, any two subgraphs intersect in an independent set of size at most 1 + O(n3=m2), which is shown to be asymptotically optimal.

Original languageEnglish
JournalElectronic Journal of Combinatorics
Volume20
Issue number1
DOIs
StatePublished - 8 Mar 2013

Keywords

  • Edge packing
  • Induced subgraph
  • Minimum degree subgraph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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