A Solution to a Problem of Dénes: a Bijection Between Trees and Factorizations of Cyclic Permutations

In his paper [1], J. Dénes proved that the set Tn of labeled trees of n vertices and the set of representations of a given cyclic permutation (belonging to the symmetric group of order n, Sn) as a product of n - 1 transpositions have the same cardinality. In [11 is also asked the question of finding a direct bijection between these sets, which is the purpose of the following work.