Planar drawings of higher-genus graphs

Authors:
Christian A. Duncan;Michael T. Goodrich;Stephen G. Kobourov
Affiliations:
Dept. of Computer Science, Louisiana Tech Univ;Dept. of Computer Science, Univ. of California, Irvine;Dept. of Computer Science, University of Arizona
Venue:
GD'09 Proceedings of the 17th international conference on Graph Drawing
Year:
2009

Citing 6
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Abstract

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.