ON HAMILTONIAN COMPLETION PROBLEM.

Abstract

The authors define the Hamiltonian completion number of a graph G, denoted hc(G), to be the minimum number of lines that need to be added to G in order to make it Hamiltonian. The Hamiltonian completion problem asks for hc(G) and a specific Hamiltonian cycle containing hc(G) new lines. Also derived is an efficient algorithm for finding hc(T) for any tree T. A number of other general results are presented including an efficient heuristic procedure which can be used on arbitrary graphs.