Bisecting Two Subsets in 3-Connected Graphs

Authors:
Hiroshi Nagamochi;Tibor Jordán;Yoshitaka Nakao;Toshihide Ibaraki
Affiliations:
-;-;-;-
Venue:
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Year:
1999

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Abstract

Given two subsets T1 and T2 of vertices in a 3-connected graph G = (V, E), where |T1| and |T2| are even numbers, we show that V can be partitioned into two sets V1 and V2 such that the graphs induced by V1 and V2 are both connected and |V1 ∩ Tj| = |V2 ∩ Tj| = |Tj|/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 Rk-1 and prove that for k = 3 such embedding always exists.