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

^*Corresponding author for this work

Institute of Software Technology (7160)

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

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.

Original language	English
Title of host publication	Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers
Editors	Patrizio Angelini, Reinhard von Hanxleden
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	16-24
Number of pages	9
ISBN (Electronic)	978-303122202-3
ISBN (Print)	9783031222023
DOIs	https://doi.org/10.1007/978-3-031-22203-0_2
Publication status	Published - 2023
Event	30th International Symposium on Graph Drawing and Network Visualization: GD 2022 - Tokyo, Japan Duration: 13 Sept 2022 → 16 Jan 2023

Publication series

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

Conference

Conference	30th International Symposium on Graph Drawing and Network Visualization
Abbreviated title	GD 2022
Country/Territory	Japan
City	Tokyo
Period	13/09/22 → 16/01/23

Keywords

Compatibility graph
Plane spanning tree
Simple drawing

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Fields of Expertise

Information, Communication & Computing

Access to Document

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

Cite this

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 (Eds.), Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers (pp. 16-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 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. ed. / Patrizio Angelini; Reinhard von Hanxleden. Springer Science and Business Media Deutschland GmbH, 2023. p. 16-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13764 LNCS).

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

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 (eds), 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), vol. 13764 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 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, editors, 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. p. 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. editor / Patrizio Angelini ; Reinhard von Hanxleden. Springer Science and Business Media Deutschland GmbH, 2023. pp. 16-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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AU - Aichholzer, Oswin

AU - Knorr, Kristin

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AU - Paul, Rosna

AU - M. Reddy, Meghana

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Compatible Spanning Trees in Simple Drawings of Kn

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Keywords

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Fields of Expertise

Access to Document

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Doctoral Program: Discrete Mathematics

FWF - ArrDra - Arrangements and Drawings