Edgeless Graph is Bipartite
Jump to navigation
Jump to search
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.
$\blacksquare$