Bipartition of a graph
= Bipartition of a graph
{title2=$V=X\sqcup Y$}
= Bipartition
{synonym}
A <bipartition> of a <graph> divides its <vertex set> into two <independent sets>, so every <edge> joins different parts. A <graph> admitting such a <partition of a set> is a <bipartite graph>. The two parts are not generally unique: separate <connected components of a graph> can have their sides exchanged independently, and <isolated vertices> can be assigned to either part.