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
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. |
| Divisions: | Management |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 13 Apr 2011 10:51 |
| Last Modified: | 11 Dec 2024 23:35 |
| URI: | http://eprints.lse.ac.uk/id/eprint/35407 |
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