Bipartite graph, a graph in which the vertices are partitioned into two sets and every edge has an endpoint in each set
Bipartite network projection is an extensively used method for compressing information about bipartite networks.
More precisely, the problem is polynomial-time if the graph is 2-colorable, that is, it is bipartite, and is NP-complete otherwise.
Many subclasses of weighted constraint satisfaction problems that are tractable by virtue of the numerical structure of their weighted constraints have associated constraint composite graphs that are bipartite in nature.
The graph representing the result of this transformation is bipartite, as all constraints are between a new and an old variable.
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Soon after, Valiant found holographic algorithms with reductions to matchgates for #Pl-Rtw-Mon-3CNF and #7Pl-3/2Bip-VC.