Question: [NP-Completeness] a) Define SPATH as the set {G, a, b, k} such that G is a graph with a path from a to b of

[NP-Completeness]

a) Define SPATH as the set {G, a, b, k} such that G is a graph with a path from a to b of length at most k. Show that SPATH is in P.

b) Define LPATH as the set {G, a, b, k} such that G is a graph with a path from a to b without repeated nodes of length at least k. Show that LPATH is NP-Complete. (You may assume the NP-Completeness of HAMPATH.)

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