Drawing a disconnected graph on the torus (Extended abstract)

Abstract

We study drawings of graphs on the torus with crossings allowed. A question posed in [M.

DeVos, B. Mohar, and R. Šámal, Unexpected behaviour of crossing sequences, J.

Combin. Theory Ser.

B 101 (2011), no. 6, 448-463], specialized to the case of the torus, asks, whether for every disconnected graph there is a drawing in the torus with the minimal number of crossings, such that one of the graphs is drawn in a planar disc. We reduce the problem to an interesting question from the geometry of numbers and solve a special case.

Keywords

• graph drawing
• crossing number
• torus
• disconnected graph