Let
G be a simple graph and
Gc be the complement of
G. Let ω(
G) denote the number of components of
G. As in Catlin et al. (1992), for a nontrivial graph
G, the
strength of
G is
Formula Not Shown where the minimum is over all subsets
S
E(
G) such that ω(
G −
S) > ω(
G). The
fractional arboricity of a nontrivial graph
G is
Formula Not Shown where the maximum runs over all subgraphs
H with
V(
H)
![](/images/glyphs/BDK.GIF)
> ω(
H).