Compatible Spanning Trees in Simple Drawings of Kn

Oswin Aichholzer; Kristin Knorr; Wolfgang Mulzer; Nicolas El Maalouly; Johannes Obenaus; Rosna Paul; Meghana M. Reddy; Birgit Vogtenhuber; Alexandra Weinberger

doi:10.1007/978-3-031-22203-0_2

Compatible Spanning Trees in Simple Drawings of Kn

Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer, Nicolas El Maalouly, Johannes Obenaus, Rosna Paul^*, Meghana M. Reddy, Birgit Vogtenhuber, Alexandra Weinberger

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Softwaretechnologie (7160)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Abstract

For a simple drawing D of the complete graph K_n, two (plane) subdrawings are compatible if their union is plane. Let T_D be the set of all plane spanning trees on D and F(T_D) be the compatibility graph that has a vertex for each element in T_D and two vertices are adjacent if and only if the corresponding trees are compatible. We show, on the one hand, that F(T_D) is connected if D is a cylindrical, monotone, or strongly c-monotone drawing. On the other hand, we show that the subgraph of F(T_D) induced by stars, double stars, and twin stars is also connected. In all cases the diameter of the corresponding compatibility graph is at most linear in n.

Originalsprache	englisch
Titel	Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers
Redakteure/-innen	Patrizio Angelini, Reinhard von Hanxleden
Herausgeber (Verlag)	Springer Science and Business Media Deutschland GmbH
Seiten	16-24
Seitenumfang	9
ISBN (elektronisch)	978-303122202-3
ISBN (Print)	9783031222023
DOIs	https://doi.org/10.1007/978-3-031-22203-0_2
Publikationsstatus	Veröffentlicht - 2023
Veranstaltung	30th International Symposium on Graph Drawing and Network Visualization: GD 2022 - Tokyo, Japan Dauer: 13 Sept. 2022 → 16 Jan. 2023

Publikationsreihe

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Band	13764 LNCS
ISSN (Print)	0302-9743
ISSN (elektronisch)	1611-3349

Konferenz

Konferenz	30th International Symposium on Graph Drawing and Network Visualization
Kurztitel	GD 2022
Land/Gebiet	Japan
Ort	Tokyo
Zeitraum	13/09/22 → 16/01/23

ASJC Scopus subject areas

Theoretische Informatik
Allgemeine Computerwissenschaft

Fields of Expertise

Information, Communication & Computing

Zugriff auf Dokument

10.1007/978-3-031-22203-0_2

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

1 Abgeschlossen
1 Laufend

DK Diskrete Mathematik
Ebner, O., Lehner, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D., Berkes, I. & Kerber, M.
1/05/10 → 30/06/24
Projekt: Forschungsprojekt
FWF - ArrDra - Arrangements und Graphenzeichnen
Vogtenhuber, B.
27/08/18 → 26/08/21
Projekt: Forschungsprojekt

Compatible Spanning Trees in Simple Drawings of Kn
Rosna Paul (Redner/in)
13 Sept. 2022 → 16 Sept. 2022
Aktivität: Vortrag oder Präsentation › Vortrag bei Konferenz oder Fachtagung › Science to science

Dieses zitieren

Aichholzer, O., Knorr, K., Mulzer, W., El Maalouly, N., Obenaus, J., Paul, R., M. Reddy, M., Vogtenhuber, B., & Weinberger, A. (2023). Compatible Spanning Trees in Simple Drawings of Kn. in P. Angelini, & R. von Hanxleden (Hrsg.), Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers (S. 16-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 13764 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-22203-0_2

Compatible Spanning Trees in Simple Drawings of Kn. / Aichholzer, Oswin; Knorr, Kristin; Mulzer, Wolfgang et al.
Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers. Hrsg. / Patrizio Angelini; Reinhard von Hanxleden. Springer Science and Business Media Deutschland GmbH, 2023. S. 16-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 13764 LNCS).

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Aichholzer, O, Knorr, K, Mulzer, W, El Maalouly, N, Obenaus, J, Paul, R, M. Reddy, M, Vogtenhuber, B & Weinberger, A 2023, Compatible Spanning Trees in Simple Drawings of Kn. in P Angelini & R von Hanxleden (Hrsg.), Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bd. 13764 LNCS, Springer Science and Business Media Deutschland GmbH, S. 16-24, 30th International Symposium on Graph Drawing and Network Visualization, Tokyo, Japan, 13/09/22. https://doi.org/10.1007/978-3-031-22203-0_2

Aichholzer O, Knorr K, Mulzer W, El Maalouly N, Obenaus J, Paul R et al. Compatible Spanning Trees in Simple Drawings of Kn. in Angelini P, von Hanxleden R, Hrsg., Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2023. S. 16-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-22203-0_2

Aichholzer, Oswin ; Knorr, Kristin ; Mulzer, Wolfgang et al. / Compatible Spanning Trees in Simple Drawings of Kn. Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers. Hrsg. / Patrizio Angelini ; Reinhard von Hanxleden. Springer Science and Business Media Deutschland GmbH, 2023. S. 16-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Compatible Spanning Trees in Simple Drawings of Kn",

abstract = "For a simple drawing D of the complete graph Kn, two (plane) subdrawings are compatible if their union is plane. Let TD be the set of all plane spanning trees on D and F(TD) be the compatibility graph that has a vertex for each element in TD and two vertices are adjacent if and only if the corresponding trees are compatible. We show, on the one hand, that F(TD) is connected if D is a cylindrical, monotone, or strongly c-monotone drawing. On the other hand, we show that the subgraph of F(TD) induced by stars, double stars, and twin stars is also connected. In all cases the diameter of the corresponding compatibility graph is at most linear in n.",

keywords = "Compatibility graph, Plane spanning tree, Simple drawing",

author = "Oswin Aichholzer and Kristin Knorr and Wolfgang Mulzer and {El Maalouly}, Nicolas and Johannes Obenaus and Rosna Paul and {M. Reddy}, Meghana and Birgit Vogtenhuber and Alexandra Weinberger",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 30th International Symposium on Graph Drawing and Network Visualization : GD 2022, GD 2022 ; Conference date: 13-09-2022 Through 16-01-2023",

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T1 - Compatible Spanning Trees in Simple Drawings of Kn

AU - Aichholzer, Oswin

AU - Knorr, Kristin

AU - Mulzer, Wolfgang

AU - El Maalouly, Nicolas

AU - Obenaus, Johannes

AU - Paul, Rosna

AU - M. Reddy, Meghana

AU - Vogtenhuber, Birgit

AU - Weinberger, Alexandra

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N2 - For a simple drawing D of the complete graph Kn, two (plane) subdrawings are compatible if their union is plane. Let TD be the set of all plane spanning trees on D and F(TD) be the compatibility graph that has a vertex for each element in TD and two vertices are adjacent if and only if the corresponding trees are compatible. We show, on the one hand, that F(TD) is connected if D is a cylindrical, monotone, or strongly c-monotone drawing. On the other hand, we show that the subgraph of F(TD) induced by stars, double stars, and twin stars is also connected. In all cases the diameter of the corresponding compatibility graph is at most linear in n.

AB - For a simple drawing D of the complete graph Kn, two (plane) subdrawings are compatible if their union is plane. Let TD be the set of all plane spanning trees on D and F(TD) be the compatibility graph that has a vertex for each element in TD and two vertices are adjacent if and only if the corresponding trees are compatible. We show, on the one hand, that F(TD) is connected if D is a cylindrical, monotone, or strongly c-monotone drawing. On the other hand, we show that the subgraph of F(TD) induced by stars, double stars, and twin stars is also connected. In all cases the diameter of the corresponding compatibility graph is at most linear in n.

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PB - Springer Science and Business Media Deutschland GmbH

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Compatible Spanning Trees in Simple Drawings of Kn

Abstract

Publikationsreihe

Konferenz

ASJC Scopus subject areas

Fields of Expertise

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Projekte

DK Diskrete Mathematik

FWF - ArrDra - Arrangements und Graphenzeichnen

Aktivitäten

Compatible Spanning Trees in Simple Drawings of Kn

Dieses zitieren