Layered Fan-Planar Graph Drawings

Therese C. Biedl; Steven Chaplick; Kaufmann Michael; Fabrizio Montecchiani; Martin Nöllenburg; Chrysanthi N. Raftopoulou

doi:10.4230/LIPICS.MFCS.2020.14

Layered Fan-Planar Graph Drawings

Therese C. Biedl, Steven Chaplick, Kaufmann Michael, Fabrizio Montecchiani, Martin Nöllenburg, Chrysanthi N. Raftopoulou

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Abstract

In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.

Original language	English
Title of host publication	45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Editors	Javier Esparza, Daniel Kral
Place of Publication	Dagstuhl, Germany
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	14:1-14:13
Volume	170
ISBN (Print)	978-3-95977-159-7
DOIs	https://doi.org/10.4230/LIPICS.MFCS.2020.14
Publication status	Published - 2020
Event	45th International Symposium on Mathematical Foundations of Computer Science - Online, Prague, Czech Republic Duration: 24 Aug 2020 → 28 Aug 2020 Conference number: 45 http://mfcs.mff.cuni.cz/2020/

Publication series

Series	Leibniz International Proceedings in Informatics (LIPIcs)
ISSN	1868-8969

Symposium

Symposium	45th International Symposium on Mathematical Foundations of Computer Science
Abbreviated title	MFCS 2020
Country/Territory	Czech Republic
City	Prague
Period	24/08/20 → 28/08/20
Internet address	http://mfcs.mff.cuni.cz/2020/

Access to Document

10.4230/LIPICS.MFCS.2020.14

1 Preprint

On Layered Fan-Planar Graph Drawings
Biedl, T. C., Chaplick, S., Fiala, J., Michael, K., Montecchiani, F., Nöllenburg, M. & Raftopoulou, C. N., 2020.
Research output: Working paper / Preprint › Preprint

Cite this

Biedl, T. C., Chaplick, S., Michael, K., Montecchiani, F., Nöllenburg, M., & Raftopoulou, C. N. (2020). Layered Fan-Planar Graph Drawings. In J. Esparza, & D. Kral (Eds.), 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) (Vol. 170, pp. 14:1-14:13). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPICS.MFCS.2020.14

Biedl, Therese C. ; Chaplick, Steven ; Michael, Kaufmann et al. / Layered Fan-Planar Graph Drawings. 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). editor / Javier Esparza ; Daniel Kral. Vol. 170 Dagstuhl, Germany : Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. pp. 14:1-14:13 (Leibniz International Proceedings in Informatics (LIPIcs)).

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Biedl, TC, Chaplick, S, Michael, K, Montecchiani, F, Nöllenburg, M & Raftopoulou, CN 2020, Layered Fan-Planar Graph Drawings. in J Esparza & D Kral (eds), 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). vol. 170, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Dagstuhl, Germany, Leibniz International Proceedings in Informatics (LIPIcs), pp. 14:1-14:13, 45th International Symposium on Mathematical Foundations of Computer Science, Prague, Czech Republic, 24/08/20. https://doi.org/10.4230/LIPICS.MFCS.2020.14

Layered Fan-Planar Graph Drawings. / Biedl, Therese C.; Chaplick, Steven; Michael, Kaufmann et al.
45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). ed. / Javier Esparza; Daniel Kral. Vol. 170 Dagstuhl, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. p. 14:1-14:13 (Leibniz International Proceedings in Informatics (LIPIcs)).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Layered Fan-Planar Graph Drawings

AU - Biedl, Therese C.

AU - Chaplick, Steven

AU - Michael, Kaufmann

AU - Montecchiani, Fabrizio

AU - Nöllenburg, Martin

AU - Raftopoulou, Chrysanthi N.

N1 - Conference code: 45

PY - 2020

Y1 - 2020

N2 - In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.

AB - In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.

U2 - 10.4230/LIPICS.MFCS.2020.14

DO - 10.4230/LIPICS.MFCS.2020.14

M3 - Chapter

SN - 978-3-95977-159-7

VL - 170

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 14:1-14:13

BT - 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

A2 - Esparza, Javier

A2 - Kral, Daniel

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

CY - Dagstuhl, Germany

T2 - 45th International Symposium on Mathematical Foundations of Computer Science

Y2 - 24 August 2020 through 28 August 2020

ER -

Biedl TC, Chaplick S, Michael K, Montecchiani F, Nöllenburg M, Raftopoulou CN. Layered Fan-Planar Graph Drawings. In Esparza J, Kral D, editors, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Vol. 170. Dagstuhl, Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2020. p. 14:1-14:13. (Leibniz International Proceedings in Informatics (LIPIcs)). doi: 10.4230/LIPICS.MFCS.2020.14

Layered Fan-Planar Graph Drawings

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On Layered Fan-Planar Graph Drawings

Cite this