Let τ (G) denote the number of vertices in a longest path of the graph G and let k 1 and k 2 be positive integers such that τ (G) = k 1 +k 2. The question at hand is whether the vertex set V (G) can be partitioned into two subsets V 1 and V 2 such that τ (G[V 1 ]) ≤ k 1 and τ (G[V 2 ]) ≤ k 2. We show that several classes of graphs have this partition property.
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