# K-partite graph

An undirected graph $G=(V,E)$ is called k-partite, if there is a partition of $V$, hereinafter referred to as $V=\dot\cup_{i=1}^k V_{i}$, such that there is no edge between two nodes that belong to the same partition component $V_{i}$. In other words, the following implication must hold:
$\forall i\in \{1,\ldots,k\}: v \in V_i \wedge w \in V_i \rightarrow \{v,w\} \not\in E$.
For $k=2$, $G$ is called bipartite graph.