# Cut set, confusing definition

I'm learning Graph Theory from Introduction to Graph Theory by Robin J. Wilson.

In chapter 3 he defines disconecting set and gives an example as follows:

See definition and example.

Then, he defines cutset in terms of desconecting set, like this:

See definition here.

*When he says "in the above example" he refers to the example in the first image.

After defining cutset, he states that $$\{ e_3, e_6, e_7, e_8 \}$$ is a cutset of the exemplifying graph; nonehtheless, $$\{ e_3, e_4, e_6, e_7, e_8 \}$$ is also a disconnecting set, and $$\{ e_3, e_6, e_7, e_8 \} ⊂ \{ e_3, e_4, e_6, e_7, e_8 \}$$, so, according to the definition of cutset $$\{ e_3, e_6, e_7, e_8 \}$$ can't be one, contradictory.

I'm sure there's something I'm not getting from that definition ¿Could you provide me with a better defition of cutset than the one in the book, or explain to me what I seem not to be getting?

• A cutset is a minimal disconnecting set. It is not supposed to have any disconnecting subsets, so $\{e_3,e_6,e_7,e_8\}$ is ok. Nov 19, 2019 at 23:03