The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle. While the notation is not standardized, Riskin denotes the Klein bottle crossing number of G as ((c r_2)^_)^_. The best known example of a graph with nonzero Klein bottle crossing number is the complete graph K_7, which can be embedded on a torus (i.e., it has toroidal crossing number 0) but not on a Klein bottle.

graph crossing number | Klein bottle | projective plane crossing number | rectilinear crossing number | toroidal crossing number

Felix Klein