Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees

S. Chaplick; Giordano Da Lozzo; Emilio Di Giacomo; Giuseppe Liotta; Fabrizio Montecchiani

doi:10.1007/978-3-030-83508-8_20

Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees

S. Chaplick, Giordano Da Lozzo^*, Emilio Di Giacomo, Giuseppe Liotta, Fabrizio Montecchiani

^*Corresponding author for this work

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

Abstract

The planar slope number psn(G) of a planar graph G is the minimum number of edge slopes in a planar straight-line drawing of G. It is known that psn(G) epsilon O(c(Delta)) for every planar graph G of degree Delta. This upper bound has been improved to O(Delta(5)) if G has treewidth three, and to O(Delta) if G has treewidth two. In this paper we prove psn(G) epsilon Theta(Delta) when G is a Halin graph, and thus has treewidth three. Furthermore, we present the first polynomial upper bound on the planar slope number for a family of graphs having treewidth four. Namely we show that O(Delta(2)) slopes suffice for nested pseudotrees.

Original language	English
Title of host publication	ALGORITHMS AND DATA STRUCTURES, WADS 2021
Editors	A Lubiw, M Salavatipour
Publisher	Springer Nature
Pages	271-285
Number of pages	15
Volume	12808
ISBN (Print)	9783030835071
DOIs	https://doi.org/10.1007/978-3-030-83508-8_20
Publication status	Published - 2021
Event	17th International Symposium on Algorithms and Data Structures - Online, Dalhousie University, Halifax, Canada Duration: 9 Aug 2021 → 11 Aug 2021 Conference number: 17 https://projects.cs.dal.ca/wads2021/

Publication series

Series	Lecture Notes in Computer Science
Volume	12808
ISSN	0302-9743

Symposium

Symposium	17th International Symposium on Algorithms and Data Structures
Abbreviated title	WADS 2021
Country/Territory	Canada
City	Halifax
Period	9/08/21 → 11/08/21
Internet address	https://projects.cs.dal.ca/wads2021/

Access to Document

10.1007/978-3-030-83508-8_20

http://arxiv.org/pdf/2105.08124

1 Preprint

Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees
Chaplick, S., Lozzo, G. D., Giacomo, E. D., Liotta, G. & Montecchiani, F., 17 May 2021.
Research output: Working paper / Preprint › Preprint

Cite this

@inproceedings{84696ba1e33e4a77a25c7a2c91c860f3,

title = "Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees",

abstract = "The planar slope number psn(G) of a planar graph G is the minimum number of edge slopes in a planar straight-line drawing of G. It is known that psn(G) epsilon O(c(Delta)) for every planar graph G of degree Delta. This upper bound has been improved to O(Delta(5)) if G has treewidth three, and to O(Delta) if G has treewidth two. In this paper we prove psn(G) epsilon Theta(Delta) when G is a Halin graph, and thus has treewidth three. Furthermore, we present the first polynomial upper bound on the planar slope number for a family of graphs having treewidth four. Namely we show that O(Delta(2)) slopes suffice for nested pseudotrees.",

author = "S. Chaplick and {Da Lozzo}, Giordano and {Di Giacomo}, Emilio and Giuseppe Liotta and Fabrizio Montecchiani",

note = "Funding Information: This work began at the Graph and Network Visualization Workshop 2019. Research by GDL was partially supported by MIUR Project “AHeAD” under PRIN 20174LF3T8, by H2020-MSCA-RISE project 734922 – “CONNECT”, and by Roma Tre University Azione 4 Project “GeoView”. Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 17th International Symposium on Algorithms and Data Structures, WADS 2021 ; Conference date: 09-08-2021 Through 11-08-2021",

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doi = "10.1007/978-3-030-83508-8_20",

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Chaplick, S, Da Lozzo, G, Di Giacomo, E, Liotta, G & Montecchiani, F 2021, Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees. in A Lubiw & M Salavatipour (eds), ALGORITHMS AND DATA STRUCTURES, WADS 2021. vol. 12808, Springer Nature, Lecture Notes in Computer Science, vol. 12808, pp. 271-285, 17th International Symposium on Algorithms and Data Structures, Halifax, Nova Scotia, Canada, 9/08/21. https://doi.org/10.1007/978-3-030-83508-8_20

Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees. / Chaplick, S.; Da Lozzo, Giordano; Di Giacomo, Emilio et al.
ALGORITHMS AND DATA STRUCTURES, WADS 2021. ed. / A Lubiw; M Salavatipour. Vol. 12808 Springer Nature, 2021. p. 271-285 (Lecture Notes in Computer Science, Vol. 12808).

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

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