Planar Drawings of Higher-Genus Graphs
Duncan, Christian A. and Goodrich, Michael T. and Kobourov, Stephen G. (2010) Planar Drawings of Higher-Genus Graphs. In: Graph Drawing 17th International Symposium, GD 2009, September 22-25, 2009, Chicago, IL, USA , pp. 45-56 (Official URL: http://dx.doi.org/10.1007/978-3-642-11805-0_7).
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In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R2 , with a bounding face deﬁned by a polygonal schema P for S. Our drawings are planar, but they allow for multiple copies of vertices and edges on 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.
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