Planar Drawings of Higher-Genus Graphs
- Cite this paper as:
- Duncan C.A., Goodrich M.T., Kobourov S.G. (2010) Planar Drawings of Higher-Genus Graphs. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface \(\cal S\) of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema \(\cal P\) for \(\cal S\). Our drawings are planar, but they allow for multiple copies of vertices and edges on \(\cal P\)’s boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.