# Hamiltonian Path Problem Multiple choice Questions and Answers (MCQs)

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## Hamiltonian Path Problem Multiple choice Questions and Answers (MCQs)

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 Question 6 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
Who formulated the first ever algorithm for solving the Hamiltonian path problem?
 A Martello B Monte Carlo C Leonard D Bellman
Question 6 Explanation:
The first ever problem to solve the Hamiltonian path was the enumerative algorithm formulated by Martello.

 Question 7 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
In what time can the Hamiltonian path problem can be solved using dynamic programming?
 A O(N) B O(N log N) C O(N2) D O(N2 2N)
Question 7 Explanation:
Using dynamic programming, the time taken to solve the Hamiltonian path problem is mathematically found to be O(N2 2N).

 Question 8 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.
 A true B false
Question 8 Explanation:
According to a handshaking lemma, in graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

 Question 9 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
Who invented the inclusion-exclusion principle to solve the Hamiltonian path problem?
 A Karp B Leonard Adleman C Andreas Bjorklund D Martello
Question 9 Explanation:
Andreas Bjorklund came up with the inclusion-exclusion principle to reduce the counting of number of Hamiltonian cycles.

 Question 10 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER]
For a graph of degree three, in what time can a Hamiltonian path be found?
 A O(0.251n) B O(0.401n) C O(0.167n) D O(0.151n)
Question 10 Explanation:
For a graph of maximum degree three, a Hamiltonian path can be found in time O(0.251n).

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