What are the differences between Hamiltonian and Eulerian paths?

What are the differences between Hamiltonian and Eulerian paths?

Hamiltonian paths visit every vertex exactly once, while Eulerian paths traverse every edge exactly once.

Can you give me an example of each?

Sure! A Hamiltonian path could be a route through a city visiting each landmark once. An Eulerian path could be a route that covers every street in a neighborhood without retracing any.

Are there specific conditions for a graph to have these paths?

Yes! A graph has a Hamiltonian path if there's a way to visit all vertices once. For an Eulerian path, it must have either zero or two vertices of odd degree.

How do these concepts apply in real-world scenarios?

They apply in routing problems, like optimizing delivery routes (Hamiltonian) or ensuring all roads are covered (Eulerian).