Cycle decomposition (graph theory)
Encyclopedia
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
.
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a cycle decomposition is a partitioning
Partition of a set
In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...
of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle
Cycle (graph theory)
In graph theory, the term cycle may refer to a closed path. If repeated vertices are allowed, it is more often called a closed walk. If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a simple cycle, circuit, circle,...
.