Fringe analysis of plane trees related to cutting and pruning
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DOI: 10.1007/s00010-017-0529-0
Abstract: Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations… read more here.
Keywords: plane trees; fringe analysis; related cutting; trees related ... See more keywords
k-Protected Vertices in Unlabeled Rooted Plane Trees
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DOI: 10.1007/s00373-017-1772-9
Abstract: We find a simple, closed formula for the proportion of vertices which are k-protected in all unlabeled rooted plane trees on n vertices. We also find that, as n goes to infinity, the average rank… read more here.
Keywords: vertices unlabeled; plane trees; rooted plane; unlabeled rooted ... See more keywords
Counting Vertices with Given Outdegree in Plane Trees and k-ary Trees
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DOI: 10.1007/s00373-018-1975-8
Abstract: We count the number of vertices with given outdegree in plane trees and k-ary trees, and get the following results: the total number of vertices of outdegree i among all plane trees with n edges… read more here.
Keywords: vertices given; plane trees; ary trees; number vertices ... See more keywords