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.

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