K Partite

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A graph $G=(V,E)$ is k-partite for some $k\in \N$ if the vertex set $V$ can be partitioned into $k$ sets $V_1$, ... $V_k$, such that each $V_i$ has no edges. In other words, $V_i^2 \cap E = \{\}$.

Special cases are tri-partite and bi-partite.

A graph is $k$-colourable iff it is k-partite.

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