Crossing numbers of complete bipartite graphs and complete graphs - Hebbar, Sanjith; Mangam, Tabitha Agnes (International Journal of Engineering and Technology, 2018)
The crossing number of a graph is the smallest number of two edge crossings over all planar representations of the graph. In this paper, we investigate the crossing numbers of complete bipartite and complete graphs. Further, we identify optimal drawings and present results on crossing numbers of these classes of graphs. In addition, Zarankiewicz’s conjecture on complete bipartite graphs and Guy’s conjecture on complete graphs are verified to be true.