  We consider self-avoiding walk on a tree with random conductances. It is
proven that in the weak disorder regime, the quenched critical point is equal
to the annealed one, and that in the strong disorder regime, these critical
points are strictly different. Derrida and Spohn, and Baffet, Patrick and
Pul$\acute{\rm e}$ give the exact value of the quenched critical point. We give
another heuristic approach by the fractional moment estimate.
