is the set of all $k$-element subsets of $A$. We write $A^c$ for the complement of $A$ (relative to some universe).

### Graphs

For graphs, we follow the notation from [@Diestel], although we will restate the most important definitions here.

A *graph* is a tuple $(V,E)$, where $V$ is the finite set of *vertices* and $E \subseteq \binom{V}{2}$ is the set of *edges*. The *endpoints* of an edge are its elements, and the edge is *incident* to them and only them. Two edges are *coincident* if they intersect, and two vertices $u$ and $v$ are *adjacent* if $\{u,v\}\in E$. If $G$ is a graph, then we write $V(G)$ for its vertex set and $E(G)$ for its edge set. A graph $H=(V',E')$ is a *subgraph* of $G=(V,E)$, written $H\subseteq G$, if $V'\subseteq V$ and $E'\subseteq E$.

For a graph $G=(V,E)$ and an arbitrary $e\in \binom{V}{2}$, we write $G + e$ and $G-e$ for the graphs $(V,E \cup \{e\})$ and $(V,E\setminus \{e\})$. If $G=(V,E)$ and $H=(V',E')$ are graphs, then $G\cup H$ denotes the graph $(V\cup V', E\cup E')$.

The *complete graph on $n$ vertices* is the graph with vertex set $[n]$ and edge set $\binom{[n]}{2}$. It is denoted by $K_n$.

Given a 