Abstract
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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References
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 9–17, 2007.
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Adrianov, N.M. On plane trees with a prescribed number of valency set realizations. J Math Sci 158, 5–10 (2009). https://doi.org/10.1007/s10958-009-9369-3
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DOI: https://doi.org/10.1007/s10958-009-9369-3