What is the difference between Hamiltonian and Eulerian paths?

What is the difference between Hamiltonian and Eulerian paths?

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

Can you give me an example of each?

Sure! A Hamiltonian path in a triangle graph visits each vertex once, while an Eulerian path in a square visits each edge.

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

Yes, a graph has a Hamiltonian path if it has enough vertices and edges, while an Eulerian path exists if at most two vertices have an odd degree.

How do I determine if a graph has a Hamiltonian or Eulerian path?

You can use various algorithms and theorems, like the Fleury's algorithm for Eulerian paths, or backtracking for Hamiltonian paths.