What is "-decomposability"

In graph theory, the (a, b)-decomposability of an undirected graph is the existence of a partition of its edges into a + 1 sets, each one of them inducing a forest, except one who 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.