Hamiltonian cycle

What is a Hamiltonian cycle?
What is a Euler cycle?
What is a minimum length Hamiltonian cycle?
Given a graph with n edges, what is the time complexity of finding a Euler path? Is this a polynomial time
algorithm? Explain and show all work and the graph. Hint: Include the algorithm and pseudocode.
Given a graph with n edges, can one find a minimum Hamiltonian cycle (TSP) in polynomial time? Has anyone
ever proved that a polynomial time algorithm does not exist for this problem? Explain your answers and show
the graph. Hint: Consider NP complete problems.
Offer one example of an IT or computer application that can be modeled as the TSP problem.

Sample Solution