The paper gives three different ways of producing the one-to-one correspondence between planted plane trees' and trivalent planted plane trees discovered by Harary, Prins, and Tutte.

In a recent paper [2], Harary, Prins, and Tutte observed two classes of trees with the same enumeration function, and indeed they succeeded in establishing a one-to-one correspondence between those two classes. The description of this correspondence, however, was quite complicated. In this note we give three different descriptions of the same correspondence. It will be comparatively easy to check that these are mutually equivalent. It is somewhat harder to check that our correspondence is (apart from a simple transformation) identical to the one described in [2], but we shall not try to do this in this paper. The classes of trees are (1) planted plane trees and (2) trivalentplanted plane trees.(A plane tree is called planted if a point of degree 1 is indicated as its root; it is called trivalent if every point has degree 1 or 3.) If n is an integer~ 2, the number of planted plane trees with n points is equal to the number of trivalent planted plane trees having n points of degree 1 (and, consequently, n--2 points of degree 3). Between these classes we wish to establish a one, to-one correspondence.