Edgeless Graph is Bipartite

Theorem

Let $N_n$ denote the edgeless graph with $n$ vertices.

Then $N_n$ is a bipartite graph.

Proof

Because $N_n$ has no edges, it has no cycles longer than $0$.

Thus in particular, it has no odd cycles.

The result follows from Graph is Bipartite iff No Odd Cycles.

$\blacksquare$