Planar and poly-arc Lombardi drawings

Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G Kobourov, Maarten Löffler

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

18 Citations (Scopus)

Abstract

In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages308-319
Number of pages12
Volume7034 LNCS
DOIs
StatePublished - 2012
Event19th International Symposium on Graph Drawing, GD 2011 - Eindhoven, Netherlands
Duration: Sep 21 2011Sep 23 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7034 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other19th International Symposium on Graph Drawing, GD 2011
CountryNetherlands
CityEindhoven
Period9/21/119/23/11

Fingerprint

Arc of a curve
Planar graph
Graph in graph theory
Planarity
Drawing

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., Eppstein, D., Goodrich, M. T., Kobourov, S. G., & Löffler, M. (2012). Planar and poly-arc Lombardi drawings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7034 LNCS, pp. 308-319). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7034 LNCS). https://doi.org/10.1007/978-3-642-25878-7_30

Planar and poly-arc Lombardi drawings. / Duncan, Christian A.; Eppstein, David; Goodrich, Michael T.; Kobourov, Stephen G; Löffler, Maarten.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. p. 308-319 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7034 LNCS).

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

Duncan, CA, Eppstein, D, Goodrich, MT, Kobourov, SG & Löffler, M 2012, Planar and poly-arc Lombardi drawings. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7034 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7034 LNCS, pp. 308-319, 19th International Symposium on Graph Drawing, GD 2011, Eindhoven, Netherlands, 9/21/11. https://doi.org/10.1007/978-3-642-25878-7_30
Duncan CA, Eppstein D, Goodrich MT, Kobourov SG, Löffler M. Planar and poly-arc Lombardi drawings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS. 2012. p. 308-319. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25878-7_30
Duncan, Christian A. ; Eppstein, David ; Goodrich, Michael T. ; Kobourov, Stephen G ; Löffler, Maarten. / Planar and poly-arc Lombardi drawings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. pp. 308-319 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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