INDEPENDENT SET: Given a graph G=(V,E)  and a positive integer k<=|V|, is there a set of vertices V' contained in V such that if u and v are in V' then the edge <u,v> is NOT in E and such that |V'|>=k? (In other words, no two vertices of V' are connected by an edge in G.)

HAMILTONIAN PATH: Given a graph G=(V,E) is there a path of the form <v1,v2><v2,v3>...<vn-1,vn> such that v1 and vn each occur once as shown, every other vertex occurs exactly twice as shown (that is, as the second of one edge and the first of another), and such that every vertex occurs in the path.