Decomposition of complete tripartite graphs into gregarious 4-cycles Original Research Article

A 4-cycle in a tripartite graph with vertex partition {V1,V2,V3} is said to be gregarious if it has at least one vertex in each Vi, 1⩽i⩽3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.