The Diameter of the Minimum Spanning Tree of a Complete Graph
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Published:2006-01-01
Issue:Proceedings
Volume:DMTCS Proceedings vol. AG,...
Page:
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ISSN:1365-8050
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Container-title:Discrete Mathematics & Theoretical Computer Science
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language:en
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Short-container-title:
Author:
Addario-Berry Louigi,Broutin Nicolas,Reed Bruce
Abstract
International audience
Let $X_1,\ldots,X_{n\choose 2}$ be independent identically distributed weights for the edges of $K_n$. If $X_i \neq X_j$ for$ i \neq j$, then there exists a unique minimum weight spanning tree $T$ of $K_n$ with these edge weights. We show that the expected diameter of $T$ is $Θ (n^{1/3})$. This settles a question of [Frieze97].
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
Discrete Mathematics and Combinatorics,General Computer Science,Theoretical Computer Science
Cited by
2 articles.
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