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A pairing of the vertices of ordered trees

✍ Scribed by Seunghyun Seo

Book ID
108315644
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
241
Category
Article
ISSN
0012-365X

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Let H n be the class of unlabeled trees with n vertices, and denote by H n a tree that is drawn uniformly at random from this set. The asymptotic behavior of the random variable deg k (H n ) that counts vertices of degree k in H n was studied, among others, by Drmota and Gittenberger in [J Graph The

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## Abstract The following interpolation theorem is proved: If a graph __G__ contains spanning trees having exactly __m__ and __n__ end‐vertices, with __m__ < __n__, then for every integer __k, m < k < n, G__ contains a spanning tree having exactly __k__ end‐vertices. This settles a problem posed by