size two with identical closed neighborhood are pairwise mds-exchangeable.

As a consequence of Lemma \[lem:SSCmitgleichemgewicht\] there can be an arbitrarily large number of stable set classes of size two with vertices of the same weight. Such an occurrence could be a problem when trying to achieve bounded kernels for the parameterized problems. But the good thing is that all of those stable set classes both see each other and see the same twin classes in the remainder of the graph. Therefore, as we will see, it is possible to reduce them to a manageable number. For a better handling we introduce the following new term. For that we define $K_{2n}-ne$ ($n\in{\ensuremath{\mathbb{N}}}$) to be the graph obtained from a complete graph on $2n$ vertices by removing $n$ disjoint edges.

Let $G=(V,E)$ be a graph and $\mathcal{S}\subseteq V$ be a maximal subset such that $G[\mathcal{S}] \cong K_{2n}-ne$ for some $n\geq 2$ and such that each vertex of $\mathcal{S}$ is adjacent to the same vertices in $V\setminus\mathcal{S}$. Then $\mathcal{S}$ is called a *stable set bundle*.

Maximal here means that no other subset fulfills the two conditions and properly contains $\mathcal{S}$. Every stable set bundle contains several stable set classes of size two. Note 