(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)