In graph theory, the (a, b)-decomposition of an undirected graph is a partition of its edges into a + 1 sets, each one of them inducing a forest, except one which induces a graph with maximum degree b.
If this graph is also a forest, then we call this a F(a, b)-decomposition.
A graph with arboricity a is (a, 0)-decomposable.
Every (a, 0)-decomposition or (a, 1)-decomposition is a F(a, 0)-decomposition or a F(a, 1)-decomposition respectively.