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An algorithm for finding a short closed spanning walk in a graph

A Hamiltonian walk of a graph is a closed spanning walk of minimum length. In this paper we generalize a Dirac type sufficient condition ensuring the existence of a Hamiltonian cycle to one ensuring the existence of a closed spanning walk of length less than a specified value. Furthermore, we present an O (p2 log p) algorithm for finding such a closed spanning walk in a graph with p vertices satisfying our condition.