Decomposition of a 2-Connected Graph into Three Connected Subgraphs
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Let n1+n2+n3 = n, and let G be a 2-connected graph on n vertices such that any 2-vertex cutset of G splits it into at most three parts. We prove that there exists a decomposition of the vertex set of G into three disjoint subsets V1, V2, V3 such that |Vi| = ni and the induced subgraph G(Vi) is connected for every i.
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