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A graph G is arbitrarily partitionable (AP for short) if for every partition (n_1, n_2, ..., n_p) of |V(G)| there exists a partition (V_1, V_2, ..., V_p) of V(G) such that each V_i induces a connected subgraph of G with order n_i. If, additionally, k of these subgraphs (k  = 1 and n &gt;= k.

Partitioning Harary graphs into connected subgraphs containing prescribed vertices