Density Conditions for k Vertex‐Disjoint Triangles in Tripartite Graphs

ABSTRACT Let be positive integers such that and be a tripartite graph with parts such that . Denote the edge densities of and by and , respectively. In this paper, we study edge density conditions for the existence of vertex‐disjoint triangles in a tripartite graph. For we give an optimal condition in terms of densities for the existence of vertex‐disjoint triangles in . We also give an optimal condition in terms of densities for the existence of a triangle‐factor in .