We provide a bijection between the set of factorizations, that is, ordered
(n-1)-tuples of transpositions in Snâ whose product is (12...n),
and labelled trees on n vertices. We prove a refinement of a theorem of
D\'{e}nes that establishes new tree-like properties of factorizations. In
particular, we show that a certain class of transpositions of a factorization
correspond naturally under our bijection to leaf edges of a tree. Moreover, we
give a generalization of this fact.Comment: 10 pages, 3 figure