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
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. |
| Uncontrolled Keywords: | minimum spanning tree, MST, Vertex connectivity, Mader's theorem, Menger's theorem, minimal k-connected graph |
| 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/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/35407/ |
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