This is intended as a survey article covering recent developments in the area of hamiltonian graphs, that is, graphs containing a spanning cycle. This article also contains some material on related topics such as traceable, harniltonian-connected and pancyclic graphs and digraphs, as well as an extensive bibliography of papers in the area.
INTRODUCTIONThe hamiltonian problem; determining when a graph contains a spanning cycle has long been fundamental in graph theory. Named for Sir William Rowan Hamilton, this problem traces its origins to the 1850s. Today, however, the flood of papers dealing with this subject and its many related problems is at its greatest; supplying us with new results as well as many new problems involving cycles and paths in graphs.To many, including myself, any path or cycle question is really a part of this general area. Although it is difficult to separate many of these ideas, for the purpose of this article, I will concentrate my efforts on results and problems dealing with spanning cycles (the classic hamiltonian problem) in ordinary graphs. I shall not attempt to survey digraphs, the traveling salesman problem (see instead [107]), or any of its related questions. However, I shall mention a few related results. I shall further restrict my attention primarily to work done since the late 1970s; however, for completeness, I shall include some earlier work in several places. For an excellent general introduction to the hamiltonian problem, the reader should see the article by
