A recurrence for certain Tutte polynomials and a depth-first search conjecture

Abstract: We combinatorially prove a recurrence between the Tutte polynomials of graphs obtained by contraction of the complete graphs $K_{n}$%. This generalizes to two variables a relation previously obtained by the author between the inversion enumerating polynomials in the colored trees. A combinatorial interpretation concerning certain polynomials recently introduced by the author via the theory of symmetric functions is also conjectured . This intrepretation uses the depth-first search.