On minimally k-edge-connected graphs and shortest k-edge-connected Steiner networks

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A graph G=(V,E) is called minimally (k,T)-edge-connected with respect to some T⊆V if there exist k-edge-disjoint paths between every pair u,vT but this property fails by deleting any edge of G. We show that |V| can be bounded by a (linear) function of k and |T| if each vertex in V-T has odd degree. We prove similar bounds in the case when G is simple and k≤3. These results are applied to prove structural properties of optimal solutions of the shortest k-edge-connected Steiner network problem. We also prove lower bounds on the corresponding Steiner ratio.

Original languageEnglish
Pages (from-to)421-432
Number of pages12
JournalDiscrete Applied Mathematics
Volume131
Issue number2
DOIs
Publication statusPublished - Sep 12 2003

Fingerprint

Steiner network
Connected graph
Structural properties
Steiner Ratio
Edge-disjoint Paths
Linear Function
Structural Properties
Optimal Solution
Odd
Lower bound
Graph in graph theory
Vertex of a graph

Keywords

  • Edge-connectivity of graphs
  • Steiner networks
  • Steiner ratio

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On minimally k-edge-connected graphs and shortest k-edge-connected Steiner networks. / Jordán, T.

In: Discrete Applied Mathematics, Vol. 131, No. 2, 12.09.2003, p. 421-432.

Research output: Contribution to journalArticle

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