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

Sorkin, Gregory B. ORCID: 0000-0003-4935-7820, 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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Identification Number: 10.1016/j.jctb.2008.08.008


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:
Additional Information: © 2008 Elsevier Inc.
Divisions: Management
Subjects: Q Science > QA Mathematics
Date Deposited: 13 Apr 2011 10:51
Last Modified: 16 May 2024 00:57

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