Triple Crossing Numbers of Graphs (Communications in Mathematical Research, 2021)
We introduce the triple crossing number, a variation of the crossingnumber, of a graph, which is the minimal number of crossing points in all drawingsof the graph with only triple crossings. It is defined to be zero for planar graphs, andto be infinite for non-planar graphs which do not admit a drawing with only triplecrossings. In this paper, we determine the triple crossing numbers for all completemultipartite graphs which include all complete graphs.
Keywords: crossing number; triple crossing number; complete multipartite graph.