Hamiltonian completion

Hamiltonian completion is a concept in graph theory related to the idea of completing a given graph into a Hamiltonian graph. A Hamiltonian graph is one that contains a Hamiltonian cycle, which is a cycle that visits every vertex in the graph exactly once and returns to the starting vertex. Hamiltonian completion specifically deals with taking an incomplete graph (one that may not be Hamiltonian) and determining whether it is possible to add a certain number of edges to make it Hamiltonian.