Hamiltonian decomposition

Hamiltonian decomposition is a concept in graph theory, particularly concerned with the decomposition of graphs into Hamiltonian cycles or paths. A **Hamiltonian cycle** is a cycle that visits every vertex of a graph exactly once and returns to the starting vertex, while a **Hamiltonian path** visits every vertex exactly once but does not return to the starting vertex. In Hamiltonian decomposition, the objective is to represent a given graph as a collection of Hamiltonian cycles or paths.