Hamilton Cycle, Traveling Salesman, Longest Path
Clique, Vertex Cover, Degree Constrained Spanning Tree, etc.
Can be converted (reduced) to each other in polynomial time.
Only known solution is to ``try every possibility'': very slow
Each possibility can be tested in polynomial time.
Solvable with concurrent/parallel execution of each possibility.
Non-determininstic polynomial time.
Any NP problem can be converted to one in the ``NP-complete'' set.