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?


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 $V_2$).


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