Bandwidths and profiles of trees

Andrew M. Odlyzko; Herbert S. Wilf

doi:10.1016/0095-8956(87)90052-9

Bandwidths and profiles of trees

Andrew M. Odlyzko, Herbert S. Wilf

Mathematics

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15 Scopus citations

Abstract

The bandwidths of labeled, rooted trees are studied. It is shown that the average bandwidth of trees of n vertices is >C₁ n and <C₂ n log n. The width of such a tree is the largest number of vertices at a constant distance from the root. The distribution of the width and its relationship with the bandwidth are studied. Results include generating functions for trees by width, and asymptotic estimates.

Original language	English (US)
Pages (from-to)	348-370
Number of pages	23
Journal	Journal of Combinatorial Theory, Series B
Volume	42
Issue number	3
DOIs	https://doi.org/10.1016/0095-8956(87)90052-9
State	Published - Jun 1987

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title = "Bandwidths and profiles of trees",

abstract = "The bandwidths of labeled, rooted trees are studied. It is shown that the average bandwidth of trees of n vertices is >C1 n and <C2 n log n. The width of such a tree is the largest number of vertices at a constant distance from the root. The distribution of the width and its relationship with the bandwidth are studied. Results include generating functions for trees by width, and asymptotic estimates.",

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AU - Odlyzko, Andrew M.

AU - Wilf, Herbert S.

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N2 - The bandwidths of labeled, rooted trees are studied. It is shown that the average bandwidth of trees of n vertices is >C1 n and <C2 n log n. The width of such a tree is the largest number of vertices at a constant distance from the root. The distribution of the width and its relationship with the bandwidth are studied. Results include generating functions for trees by width, and asymptotic estimates.

AB - The bandwidths of labeled, rooted trees are studied. It is shown that the average bandwidth of trees of n vertices is >C1 n and <C2 n log n. The width of such a tree is the largest number of vertices at a constant distance from the root. The distribution of the width and its relationship with the bandwidth are studied. Results include generating functions for trees by width, and asymptotic estimates.

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Bandwidths and profiles of trees

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