Find cycles visiting every vertex exactly once — NP-complete for general graphs
A Hamiltonian cycle visits every vertex exactly once and returns to the start. Determining existence is NP-complete (no polynomial-time algorithm known). This visualizer uses backtracking search with Ore's heuristic: if deg(u)+deg(v)≥n for all non-adjacent pairs, a Hamilton cycle exists. Click vertices to manually build a path, or use "Find Cycle" for automatic backtracking search.