Cycle decomposition

In mathematics, the term cycle decomposition can mean:

• In graph theory, a cycle decomposition is a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle.
• In group theory, a cycle decomposition is a useful convention for expressing a permutation in terms of its constituent cycles.

In commutative algebra and linear algebra, cyclic decomposition refers to writing a finitely generated module over a principal ideal domain as the direct sum of cyclic modules and one free module.