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


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 inline image edge disjoint Hamilton cycles, then there also exists a covering of its edges by inline image Hamilton cycles. This implies that for every α > 0 and every inline image there exists a covering of all edges of G(n,p) by inline image Hamilton cycles asymptotically almost surely, which is nearly optimal.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 183-200, 2014