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

Abstract

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