(Or "HAMIlton' s problem") A problem in {graph theory} posed by {William HAMIlton}: given a {graph}, is there a path through the graph which visits each vertex precisely once (a "HAMIltonian path")? Is there a HAMIltonian path which ends up where it started (a "HAMIltonian cycle" or "HAMIltonian tour")? HAMIlton' s problem is NP-complete. It has numerous applications, sometimes completely unexpected, in computing. Start . (1997-07-18)