ABSTRACT
One feature of graph theory that has helped to popularize the subject lies in its applications to the area of puzzles and games. Hamiltonian graphs are studied next and some necessary conditions and some sufficient conditions for graphs to be hamiltonian are given. However, it still remains a challenging unsolved problem to discover an elegant, useful characterization of hamiltonian graphs, rather than only a disguised paraphrase of the definition. The smallest known nonhamiltonian triply connected cubic planar graph, having 38 points, was constructed independently by J. Lederberg, J. Bosak, and D. Barnette. The apparent lack of any relationship between eulerian and hamiltonian graphs where each graph is a block with eight points. Incidentally, M. D. Plummer conjectures that the square of every 2-connected graph is hamiltonian.
