FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 6, PAGES 9-17

**On planes trees with a prescribed number of valency set
realizations**

N. M. Adrianov

Abstract

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We describe valency sets of plane bicolored trees with
a prescribed number of realizations by plane trees.
Three special types of plane trees are defined: chains, trees of
diameter $4$, and special trees of
diameter $6$.
We prove that there is a finite number of valency sets that have
$R$ realizations as
plane trees and do not belong to these special types.
The number of edges of such trees is less than or equal to $12R+2$.
The complete lists of valency sets of plane bicolored trees with
$1$, $2$, or $3$ realizations are
presented.

Location: http://mech.math.msu.su/~fpm/eng/k07/k076/k07601h.htm

Last modified: April 22, 2008