Packing Hamilton Cycles Online

Abstract

It is known that w.h.p. the hitting time $τ_{2σ}$ for the random graph process to have minimum degree $2σ$ coincides with the hitting time for $σ$ edge disjoint Hamilton cycles. In this paper we prove an online version of this property. We show that, for a fixed integer $σ\geq 2$, if random edges of $K_n$ are presented one by one then w.h.p. it is possible to color the edges online with $σ$ colors so that at time $τ_{2σ}$, each color class is Hamiltonian.

Minor changes