Planar and Poly-Arc Lombardi Drawings

Christian Duncan; David Eppstein; Michael T. Goodrich; Stephen Kobourov; Maarten Löffler

Planar and Poly-Arc Lombardi Drawings

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.

Original language	English
Title of host publication	Proc. 19th Symposium on Graph Drawing
Pages	308-319
Number of pages	12
Publication status	Published - 2011

Publication series

Name	LNCS
Volume	7034

Keywords

CG, GRAPH, GD

Access to Document

http://dx.doi.org/10.1007/978-3-642-25878-7_30

Cite this

@inproceedings{44ac788779a6404b8fafccf5a84e7aaa,

title = "Planar and Poly-Arc Lombardi Drawings",

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; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.",

keywords = "CG, GRAPH, GD",

author = "Christian Duncan and David Eppstein and Goodrich, {Michael T.} and Stephen Kobourov and Maarten L{\"o}ffler",

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language = "English",

series = "LNCS",

pages = "308--319",

booktitle = "Proc. 19th Symposium on Graph Drawing",

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T1 - Planar and Poly-Arc Lombardi Drawings

AU - Duncan, Christian

AU - Eppstein, David

AU - Goodrich, Michael T.

AU - Kobourov, Stephen

AU - Löffler, Maarten

PY - 2011

Y1 - 2011

N2 - 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; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.

AB - 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; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.

KW - CG, GRAPH, GD

M3 - Conference contribution

T3 - LNCS

SP - 308

EP - 319

BT - Proc. 19th Symposium on Graph Drawing

ER -

Planar and Poly-Arc Lombardi Drawings

Abstract

Publication series

Keywords

Access to Document

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Cite this