On covering expander graphs by hamilton cycles

Roman Glebov, Michael Krivelevich, Tibor Szabó

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume44
Issue number2
DOIs
StatePublished - Mar 2014

Keywords

  • 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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