What is a Hamiltonian cycle?
An example of an AI chatbot conversation about Hamiltonian cycles in graph theory.
What is a Hamiltonian cycle?
A Hamiltonian cycle is a path in a graph that visits each vertex exactly once and returns to the starting vertex.
Can you give me an example of a Hamiltonian cycle?
Sure! In a triangle graph with vertices A, B, and C, the cycle A -> B -> C -> A is a Hamiltonian cycle.
How do you determine if a graph has a Hamiltonian cycle?
Determining if a graph has a Hamiltonian cycle is NP-complete, meaning there's no known efficient algorithm for all cases.
Are there any practical applications of Hamiltonian cycles?
Yes, Hamiltonian cycles have applications in routing problems, such as the Traveling Salesman Problem.
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