On the k-path partition of graphs

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The k-path partition problem is to partition a graph into the minimum number of paths, so that none of them has length more than k, for a given positive integer k. The problem is a generalization of the Hamiltonian path problem and the problem of partitioning a graph into the minimum number of paths. The k-path partition problem remains NP-complete on the class of chordal bipartite graphs if k is part of the input, and we show that it is NP-complete on the class of comparability graphs even for k=3. On the positive side, we present a polynomial-time solution for the problem, with any k, on bipartite permutation graphs, which form a subclass of chordal bipartite graphs.




Steiner, G. (2003). On the k-path partition of graphs. Theoretical Computer Science, 290(3), 2147–2155. https://doi.org/10.1016/S0304-3975(02)00577-7

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