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We describe some necessary conditions for the existence of a Hamiltonian pathin any graph (in other words, for a graph to be traceable). These conditionsresult in a linear time algorithm to decide the Hamiltonian path problem forcactus graphs. We apply this algorithm to several molecular databases to reportthe numbers of graphs that are traceable cactus graphs.

Simple Necessary Conditions for the Existence of a Hamiltonian Path with Applications to Cactus Graphs