Please take a look at these definitions:
A multipartite graph is a graph of the form $K_{r_1,\ldots, r_n}$ where $n > 1$, $r_1, \ldots, r_n\ge 1$, such that
The set of nodes of the graph is the disjoint union of n sets: $V = V_1 \cup\cdots\cup V_n$, and $|V_i|=r_i$ for all $1\le i\le n$.
The set of nodes of the graph is the set of all possible connections between nodes in that do no belong to the same set $S_i$. Formally:
$E= \{(x,y)\mid x \in S_i, y \in S_j, i \ne j\}$
A graph $G$ is planar if and only if every subdivision of $G$ is planar. A graph $G$ is planar if and only if it contains no subdivision of $K_{3,3}$ or $K_5$.
I need to determine all multipartite graphs that are not planar.