# Empty Set Partition of a Bipartite Graph?

My textbook defines a bipartite graph in the following way:

A graph $G = (V, E)$ is called bipartite if $V = V_1 \cup V_2$ with $V_1 \cap V_2 = \emptyset$, and every edge of $G$ is of the form $\{a, b\}$ with $a \in V_1$ and $b \in V_2$.

So from this definition, we could have $V_1 = \emptyset$ and $V_2 = H$ where $H$ is a set of vertices with no edges. In otherwards, any graph containing only vertices and not edges is considered bipartite.

Is this true?

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Technically speaking, you could allow one or both of the partite sets to be empty, but these are degenerate cases. The typical bipartite graph has two nonempty sets of vertices $V_1$ and $V_2$ and all the edges go "across" the two partite sets (i.e. one end is in $V_1$ and one end is in $V_2$).