Trees with 1-factors and oriented trees (Q1174177)

Trees with 1-factors (or simply matched trees) are those with a complete matching of the vertices. Using the technique of the generating functions, some recursive and asymptotic formulae concerning the number of rooted, planted and unlabeled matched trees are presented. Further, a unique correspondence between the matched trees on \(2n\) vertices and oriented trees on \(n\) vertices is shown which makes possible to prove some results concerning the number of self-converse oriented trees.