Check whether a Hamiltonian path exists in a small graph via backtracking search.
A Hamiltonian path visits every vertex in a graph exactly once. A Hamiltonian cycle is a Hamiltonian path that returns to the starting vertex. This calculator uses backtracking search, which is exact but exponential in time complexity.
Backtracking: try extending the current path to each unvisited neighbor; backtrack if stuck
It is NP-complete — no known polynomial-time algorithm exists. For small graphs backtracking is feasible, but it becomes impractical for large graphs.
A Hamiltonian path visits every vertex exactly once. An Euler path traverses every edge exactly once. They are fundamentally different problems.