Really straight graph drawings

Vida Dujmović; Matthew Suderman; David R. Wood

doi:10.1007/978-3-540-31843-9_14

Really straight graph drawings

Vida Dujmović, Matthew Suderman, David R. Wood

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

Abstract

We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with script O sign(log n) slopes.

Original language	English
Title of host publication	Graph Drawing
Subtitle of host publication	12th International Symposium, GD 2004 New York, NY, USA, September 29-October 2, 2004 Revised Selected Papers
Editors	János Pach
Place of Publication	Berlin Germany
Publisher	Springer
Pages	122-132
Number of pages	11
ISBN (Print)	3540245286
DOIs	https://doi.org/10.1007/978-3-540-31843-9_14
Publication status	Published - 1 Dec 2004
Externally published	Yes
Event	Graph Drawing 2004 - New York, United States of America Duration: 29 Sept 2004 → 2 Oct 2004 Conference number: 12th https://link.springer.com/book/10.1007/b105810 (Proceedings)

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	3383
ISSN (Print)	0302-9743

Conference

Conference	Graph Drawing 2004
Abbreviated title	GD 2004
Country/Territory	United States of America
City	New York
Period	29/09/04 → 2/10/04
Internet address	https://link.springer.com/book/10.1007/b105810 (Proceedings)

Access to Document

10.1007/978-3-540-31843-9_14

Cite this

@inproceedings{d1977c252d0e413f9d80c3b069218655,

title = "Really straight graph drawings",

abstract = "We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with script O sign(log n) slopes.",

author = "Vida Dujmovi{\'c} and Matthew Suderman and Wood, {David R.}",

year = "2004",

month = dec,

day = "1",

doi = "10.1007/978-3-540-31843-9_14",

language = "English",

isbn = "3540245286",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "122--132",

editor = "J{\'a}nos Pach",

booktitle = "Graph Drawing",

note = "Graph Drawing 2004, GD 2004 ; Conference date: 29-09-2004 Through 02-10-2004",

url = "https://link.springer.com/book/10.1007/b105810",

}

Dujmović, V, Suderman, M & Wood, DR 2004, Really straight graph drawings. in J Pach (ed.), Graph Drawing: 12th International Symposium, GD 2004 New York, NY, USA, September 29-October 2, 2004 Revised Selected Papers. Lecture Notes in Computer Science, vol. 3383, Springer, Berlin Germany, pp. 122-132, Graph Drawing 2004, New York, New York, United States of America, 29/09/04. https://doi.org/10.1007/978-3-540-31843-9_14

Really straight graph drawings. / Dujmović, Vida; Suderman, Matthew; Wood, David R.
Graph Drawing: 12th International Symposium, GD 2004 New York, NY, USA, September 29-October 2, 2004 Revised Selected Papers. ed. / János Pach. Berlin Germany: Springer, 2004. p. 122-132 (Lecture Notes in Computer Science; Vol. 3383).

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

TY - GEN

T1 - Really straight graph drawings

AU - Dujmović, Vida

AU - Suderman, Matthew

AU - Wood, David R.

N1 - Conference code: 12th

PY - 2004/12/1

Y1 - 2004/12/1

N2 - We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with script O sign(log n) slopes.

AB - We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with script O sign(log n) slopes.

UR - http://www.scopus.com/inward/record.url?scp=24144455989&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-31843-9_14

DO - 10.1007/978-3-540-31843-9_14

M3 - Conference Paper

AN - SCOPUS:24144455989

SN - 3540245286

T3 - Lecture Notes in Computer Science

SP - 122

EP - 132

BT - Graph Drawing

A2 - Pach, János

PB - Springer

CY - Berlin Germany

T2 - Graph Drawing 2004

Y2 - 29 September 2004 through 2 October 2004

ER -

Really straight graph drawings

Abstract

Publication series

Conference

Access to Document

Other files and links

Cite this