On covering expander graphs by hamilton cycles

Roman Glebov, Michael Krivelevich, Tibor Szabó

Research output: Contribution to journalArticlepeer-review


The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree Δ satisfies some basic expansion properties and contains a family of (1-o(1))Δ/2 edge disjoint Hamilton cycles, then there also exists a covering of its edges by (1+o(1))Δ/2 Hamilton cycles. This implies that for every α > 0 and every p≥nα-1 there exists a covering of all edges of G(n,p) by (1+o(1))np/2 Hamilton cycles asymptotically almost surely, which is nearly optimal.

Original languageEnglish
Pages (from-to)183-200
Number of pages18
JournalRandom Structures and Algorithms
Issue number2
StatePublished - Mar 2014


  • Covering
  • Expander Graphs
  • Hamilton Covering
  • Hamilton Cycles
  • Random Graphs

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics
  • General Mathematics
  • Computer Graphics and Computer-Aided Design


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