ICS Theory Group

October 2, Fall Quarter 2009: Thoery Seminar

1:00pm in 1423 Bren Hall

Planar Drawings of Higher-Genus Graphs

Michael Goodrich, UC Irvine

In this talk, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on a surface S of genus g and produce a planar drawing of G, with a bounding face de ned 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.