Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one

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Assume that we have a graph, say $G$, with $100$ vertices, and our graph has no articulation points (a vertex that the graph will become unconnected if we remove it from the graph). Prove that we can divide vertices of $G$ into two groups ($50$ vertices each), such that the induced subgraph is connected in each group.