Capella University Graph Applications and The Traveling Salesperson Questions
Description
Define what it means for a graph to have an Euler cycle.
Provide a real-world example that can be modeled by a graph that has an Euler cycle and explain how the Euler cycle can be found.
- Given a graph with n edges, what is the time complexity of finding a Euler path? Is this a polynomial time algorithm?
- Define what it means for a graph to have a Hamiltonian cycle and minimum-length Hamiltonian cycle.
- Provide a real-world example that can be modeled by a graph that has a Hamiltonian cycle (TSP) and explain how a minimum-length Hamiltonian cycle can be found.
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?
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