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Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

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  • Toshimasa Ishii
  • Hiroshi Nagamochi
  • Toshihide Ibaraki

Abstract

Given an undirected multigraph G = (V, E) and two positive integers ℓ and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an ℓ-edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn2) time for any fixed ℓ and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G.

Suggested Citation

  • Toshimasa Ishii & Hiroshi Nagamochi & Toshihide Ibaraki, 2000. "Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 35-77, March.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:1:d:10.1023_a:1009884922499
    DOI: 10.1023/A:1009884922499
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    References listed on IDEAS

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    1. Hiroshi Nagamochi & Toshihide Ibaraki, 1997. "Deterministic Õ(nm) Time Edge-Splitting in Undirected Graphs," Journal of Combinatorial Optimization, Springer, vol. 1(1), pages 5-46, March.
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