It is known that w.h.p. the hitting time τ2σ​ 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≥2, if
random edges of Kn​ are presented one by one then w.h.p. it is possible to
color the edges online with σ colors so that at time τ2σ​,
each color class is Hamiltonian.Comment: Minor change