Question:medium
Let A be the problem of finding a Hamiltonian cycle in a graph G = (V, E) with |V| divisible by 3, and B be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?
Let A be the problem of finding a Hamiltonian cycle in a graph G = (V, E) with |V| divisible by 3, and B be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?
Show Hint
Modifying problem constraints (like divisibility) does not necessarily reduce complexity if the core problem remains NP-hard.
Updated On: Feb 11, 2026
- Both A and B are NP-hard
- A is NP-hard but B is not
- B is NP-hard but A is not
- Neither A nor B is NP-hard
Show Solution
The Correct Option is A
Solution and Explanation
- The problem of finding a Hamiltonian cycle is NP-complete; its computational complexity is not reduced even if the graph G has a vertex count (|V|) divisible by 3. - Determining the existence of such a cycle in graphs is also NP-hard, as this task is equivalent to the Hamiltonian cycle problem itself. - Consequently, both A and B are classified as NP-hard.
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