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 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages45-56
Number of pages12
Volume5849 LNCS
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Genus
Graph in graph theory
Embedded Graph
Graph Drawing
Polynomials
Polynomial-time Algorithm
Schema
Disjoint
Interior
NP-complete problem
Face
Cycle
Vertex of a graph
Drawing

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (2010). Planar drawings of higher-genus graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5849 LNCS, 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

Planar drawings of higher-genus graphs. / Duncan, Christian A.; Goodrich, Michael T.; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5849 LNCS 2010. p. 45-56 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5849 LNCS).

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

Duncan, CA, Goodrich, MT & Kobourov, SG 2010, Planar drawings of higher-genus graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5849 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5849 LNCS, pp. 45-56, 17th International Symposium on Graph Drawing, GD 2009, Chicago, IL, United States, 9/22/09. https://doi.org/10.1007/978-3-642-11805-0_7
Duncan CA, Goodrich MT, Kobourov SG. Planar drawings of higher-genus graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5849 LNCS. 2010. p. 45-56. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-11805-0_7
Duncan, Christian A. ; Goodrich, Michael T. ; Kobourov, Stephen G. / Planar drawings of higher-genus graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5849 LNCS 2010. pp. 45-56 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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