Hamilton circuit

A Hamiltonian circuit is a specific type of path in graph theory. Graph theory itself is a branch of mathematics that studies networks of points, called vertices, connected by lines, called edges.1

A Hamiltonian circuit visits every vertex in a graph exactly once and returns to the starting vertex. This is distinct from an Eulerian circuit, which traverses every edge exactly once. The concept of Hamiltonian circuits originated from a puzzle invented by Sir William Rowan Hamilton in 1859, involving a route along the edges of a dodecahedron that would pass through each corner exactly once. Unlike Eulerian graphs, which have well-defined conditions for their existence, characterizing Hamiltonian graphs remains a more challenging area of research.12