The 4-girth-thickness of the complete multipartite graph

The g -girth-thickness θ ( g ,  G ) of a graph G is the smallest number of planar subgraphs of girth at least g whose union is G . In this paper, we calculate the 4 -girth-thickness θ (4,  G ) of the complete m -partite graph G when each part has an even number of vertices.