Approximate Hamilton decompositions of random graphs

Abstract

We show that if pn ≫ log n the binomial random graph Gn,p has an approximate Hamilton decomposition. More precisely, we show that in this range Gn,p contains a set of edge-disjoint Hamilton cycles covering almost all of its edges. This is best possible in the sense that the condition that pn ≫ log n is necessary. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.