We consider the problem of recovering an unknown k-factor, hidden in a
weighted random graph. For k=1 this is the planted matching problem, while
the k=2 case is closely related to the planted travelling salesman problem.
The inference problem is solved by exploiting the information arising from the
use of two different distributions for the weights on the edges inside and
outside the planted sub-graph. We argue that, in the large size limit, a phase
transition can appear between a full and a partial recovery phase as function
of the signal-to-noise ratio. We give a criterion for the location of the
transition.Comment: 21 pages, 4 figure