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 Scopus citations

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 publicationGraph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers
Pages308-319
Number of pages12
DOIs
StatePublished - Jan 1 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

    Fingerprint

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Duncan, C. A., Eppstein, D., Goodrich, M. T., Kobourov, S. G., & Löffler, M. (2012). Planar and poly-arc Lombardi drawings. In Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers (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