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A tight bound on the collection of edges in MSTs of induced subgraphs

Sorkin, Gregory B. , Steger, Angelika and Zenklusenc, Rico (2009) A tight bound on the collection of edges in MSTs of induced subgraphs. Journal of Combinatorial Theory, Series B, 99 (2). pp. 428-435. ISSN 0095-8956

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Abstract

Let G=(V,E) be a complete n-vertex graph with distinct positive edge weights. We prove that for k{1,2,…,n−1}, the set consisting of the edges of all minimum spanning trees (MSTs) over induced subgraphs of G with n−k+1 vertices has at most elements. This proves a conjecture of Goemans and Vondrák [M.X. Goemans, J. Vondrák, Covering minimum spanning trees of random subgraphs, Random Structures Algorithms 29 (3) (2005) 257–276]. We also show that the result is a generalization of Mader's Theorem, which bounds the number of edges in any edge-minimal k-connected graph.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2008 Elsevier Inc.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 Apr 2011 10:51
URL: http://eprints.lse.ac.uk/35407/

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