Given two disjoint subsets T1 and T2 of nodes in an undirected 3-connected graph G = (V, E) with node set V and arc set 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|2log|V|) 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 an embedding always exists.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics