Question

LONG-PATH is the problem of, given (G, u, v, k) where G is a graph, u and v vertices and k an integer, determining if there is a simple path in G from u to v of length at least k.

Show that LONG-PATH is NP-complete.

EXPERT ANSWER

Consider the following given data of the problem LONG-PATH (G, u, v, k):

G = G is a graph.

u, v = are vertices of the graph.

k