Bisecting Two Subsets in 3-Connected Graphs

  • Hiroshi Nagamochi
  • Yoshitaka Nakao
  • Toshihide Ibaraki
  • Tibor Jordán
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)


Given two subsets T 1 and T 2 of vertices in a 3-connected graph G = (V,E), where |T 1| and |T 2| are even numbers, we show that V can be partitioned into two sets V 1 and V 2 such that the graphs induced by V 1 and V 2 are both connected and |V 1T j| = |V 2T j| = |T j|/2 holds for each j = 1, 2. Such a partition can be found in O(|V|2) time. Our proof relies on geometric arguments. We define a new type of ‘convex embedding’ of k-connected graphs into real space R k-1 and prove that for k = 3 such embedding always exists.


Undirected Graph Complete Bipartite Graph Convex Polytope Connected Subgraph Internal Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Hiroshi Nagamochi
    • 1
  • Yoshitaka Nakao
    • 1
  • Toshihide Ibaraki
    • 1
  • Tibor Jordán
    • 2
  1. 1.Kyoto UniversityKyotoJapan
  2. 2.BRICSUniversity of AarhusAarhus CDenmark

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