Decomposition of a 2-Connected Graph into Three Connected Subgraphs

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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.