Planar drawings of higher-genus graphs

Christian A. Duncan, Michael T. Goodrich, Stephen G. Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema for P for S. Our drawings are planar, but they allow for multiple copies of vertices and edges on '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.

Original languageEnglish (US)
Title of host publicationGraph Drawing - 17th International Symposium, GD 2009, Revised Papers
Pages45-56
Number of pages12
DOIs
StatePublished - May 3 2010
Event17th International Symposium on Graph Drawing, GD 2009 - Chicago, IL, United States
Duration: Sep 22 2009Sep 25 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5849 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Symposium on Graph Drawing, GD 2009
CountryUnited States
CityChicago, IL
Period9/22/099/25/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (2010). Planar drawings of higher-genus graphs. In Graph Drawing - 17th International Symposium, GD 2009, Revised Papers (pp. 45-56). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5849 LNCS). https://doi.org/10.1007/978-3-642-11805-0_7