A graph decomposition is a set partition of the edge set of a graph into the
edge sets of specified subgraphs.
The subgraphs may share vertices,
but each graph edge belongs to exactly one part. An
-decomposition
requires every subgraph in the decomposition to be isomorphic to 
. In particular, an odd
cycle decomposition uses cycle graphs of a fixed
odd length (Hou et al. 2026).
Graph Decomposition
See also
Cycle Double Cover, Erdős-Gallai Cycle Decomposition Conjecture, Hamilton Decomposition, Odd Cycle Decomposition, SubgraphExplore with Wolfram|Alpha
References
Hou, J.; Hu, C.; and Wang, H. "Odd Cycle Decompositions." 16 Oct 2026. https://arxiv.org/abs/2610.23471.Cite this as:
Weisstein, Eric W. "Graph Decomposition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphDecomposition.html