Statistics Internet Library's Journal

Name of theorem?
I need a theorem which tells me this, for an any finite graph G and for any reversible random walk on that graph (any transition probabilities and any transition times, in other words):

If the average time for the random walk to go from X to Y is M, there is a subgraph S without loops connecting X with Y such that the average time for the random walk conditioned to stay on S is less than M.

= = =

I don't want to prove the wheel all over again, so if anyone has a reference, and preferrably a name (these things tend to acquire names), I would be very grateful.