Prove that the following problem is NP-complete:
Two-cycle: Does G contain two cycles with the followingproperties:
(a) Each cycle is non-self-intersecting
(b) The two cycles don’t share any vertices.
(c) Each cycle is length at least 3.
(d) The sum of the lengths of the cycles is n.
For instance, if G has a simple cycle of length n/4 and one oflength 3n/4 (and they don’t touch each other) the answer is YES
Answer