What are Hamiltonian paths in graph theory?

What are Hamiltonian paths in graph theory?

Hamiltonian paths are paths in a graph that visit each vertex exactly once. They are named after Sir William Rowan Hamilton.

Can you give me an example of a Hamiltonian path?

Sure! In a simple triangle graph with vertices A, B, and C, a Hamiltonian path could be A -> B -> C.

Are there any algorithms to find Hamiltonian paths?

Yes, there are several algorithms, including backtracking and dynamic programming, but finding Hamiltonian paths is NP-complete.

What is the difference between Hamiltonian paths and cycles?

A Hamiltonian path visits each vertex once, while a Hamiltonian cycle returns to the starting vertex, forming a loop.