The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for acyclic digraphs. The detour matrix is a real symmetric matrix whose (i, j)th entry is the length of the longest path from vertex i to vertex j. For a traceable graph, longest paths correspond to Hamiltonian paths. Finding a longest path is challenging for stacked book graphs and Apollonian networks.
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