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Increasing the Edge-Connectivity by Contracting a Vertex Subset in Graphs
Hiroshi NAGAMOCHI
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E89-D
No.2
pp.744-750 Publication Date: 2006/02/01 Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e89-d.2.744 Print ISSN: 0916-8532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Graph Algorithm Keyword: algorithm, edge-connectivity, extreme vertex sets, graph, source location problem,
Full Text: PDF(532.5KB)>>
Summary:
Let G = (V,E) be an edge weighted graph with n vertices and m edges. For a given integer p with 1 < p < n, we call a set X V of p vertices a p-maximizer if X has a property that the edge-connectivity of the graph obtained by contracting X into a single vertex is no less than that of the graph obtained by contracting any other subset of p vertices. In this paper, we first show that there always exists an ordering v1,v2,...,vn of vertices in V such that, for each i = 2,3,...,n - 1, set {v1,v2,...,vi} is an i-maximizer. We give an O(mn + n2log n) time algorithm for finding such an ordering and then show an application to the source location problem.
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