Tripartite version of the Corrádi–Hajnal theorem Original Research Article

Let G be a tripartite graph with N vertices in each vertex class. If each vertex is adjacent to at least (2/3)N vertices in each of the other classes, then either G contains a subgraph that consists of N vertex-disjoint triangles or G is a specific graph in which each vertex is adjacent to exactly (2/3)N vertices in each of the other classes.