Tripartite Version of the Corr\'adi-Hajnal Theorem

Abstract

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.