Edge Partitions of Complete Geometric Graphs

Oswin Aichholzer; Johannes Obenaus; Joachim Orthaber; Rosna Paul; Patrick Schnider; Raphael Steiner; Tim Taubner; Birgit Vogtenhuber

doi:10.4230/LIPIcs.SoCG.2022.6

Edge Partitions of Complete Geometric Graphs

Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber, Rosna Paul, Patrick Schnider, Raphael Steiner, Tim Taubner, Birgit Vogtenhuber

Institute of Software Technology (7160)

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

Abstract

In this paper, we disprove the long-standing conjecture that any complete geometric graph on 2n vertices can be partitioned into n plane spanning trees. Our construction is based on so-called bumpy wheel sets. We fully characterize which bumpy wheels can and in particular which cannot be partitioned into plane spanning trees (or even into arbitrary plane subgraphs). Furthermore, we show a sufficient condition for generalized wheels to not admit a partition into plane spanning trees, and give a complete characterization when they admit a partition into plane spanning double stars. Finally, we initiate the study of partitions into beyond planar subgraphs, namely into k-planar and k-quasi-planar subgraphs and obtain first bounds on the number of subgraphs required in this setting.

Original language	English
Title of host publication	38th International Symposium on Computational Geometry (SoCG 2022)
Editors	Xavier Goaoc, Michael Kerber
Place of Publication	Dagstuhl, Germany
Publisher	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages	6:1-6:16
Volume	224
ISBN (Electronic)	9783959772273
DOIs	https://doi.org/10.4230/LIPIcs.SoCG.2022.6
Publication status	Published - 1 Jun 2022
Event	38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Germany Duration: 7 Jun 2022 → 10 Jun 2022 https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	224
ISSN (Print)	1868-8969

Conference

Conference	38th International Symposium on Computational Geometry
Abbreviated title	SoCG 2022
Country/Territory	Germany
City	Berlin
Period	7/06/22 → 10/06/22
Internet address	https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html

Keywords

complete geometric graph
edge partition
plane spanning tree
wheel set

ASJC Scopus subject areas

Software

Fields of Expertise

Information, Communication & Computing

Access to Document

10.4230/LIPIcs.SoCG.2022.6Licence: CC BY 4.0

Cite this

Aichholzer, O., Obenaus, J., Orthaber, J., Paul, R., Schnider, P., Steiner, R., Taubner, T., & Vogtenhuber, B. (2022). Edge Partitions of Complete Geometric Graphs. In X. Goaoc, & M. Kerber (Eds.), 38th International Symposium on Computational Geometry (SoCG 2022) (Vol. 224, pp. 6:1-6:16). Article 6 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 224). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2022.6

Edge Partitions of Complete Geometric Graphs. / Aichholzer, Oswin; Obenaus, Johannes; Orthaber, Joachim et al.
38th International Symposium on Computational Geometry (SoCG 2022). ed. / Xavier Goaoc; Michael Kerber. Vol. 224 Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. p. 6:1-6:16 6 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 224).

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

Aichholzer, O, Obenaus, J, Orthaber, J, Paul, R, Schnider, P, Steiner, R, Taubner, T & Vogtenhuber, B 2022, Edge Partitions of Complete Geometric Graphs. in X Goaoc & M Kerber (eds), 38th International Symposium on Computational Geometry (SoCG 2022). vol. 224, 6, Leibniz International Proceedings in Informatics, LIPIcs, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, pp. 6:1-6:16, 38th International Symposium on Computational Geometry, Berlin, Germany, 7/06/22. https://doi.org/10.4230/LIPIcs.SoCG.2022.6

Aichholzer O, Obenaus J, Orthaber J, Paul R, Schnider P, Steiner R et al. Edge Partitions of Complete Geometric Graphs. In Goaoc X, Kerber M, editors, 38th International Symposium on Computational Geometry (SoCG 2022). Vol. 224. Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. 2022. p. 6:1-6:16. 6. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.SoCG.2022.6

Aichholzer, Oswin ; Obenaus, Johannes ; Orthaber, Joachim et al. / Edge Partitions of Complete Geometric Graphs. 38th International Symposium on Computational Geometry (SoCG 2022). editor / Xavier Goaoc ; Michael Kerber. Vol. 224 Dagstuhl, Germany : Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. pp. 6:1-6:16 (Leibniz International Proceedings in Informatics, LIPIcs).

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Edge Partitions of Complete Geometric Graphs

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Doctoral Program: Discrete Mathematics

5th DACH Workshop on Arrangements and Drawings

Cite this

Edge Partitions of Complete Geometric Graphs

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Projects

Doctoral Program: Discrete Mathematics

Activities

5th DACH Workshop on Arrangements and Drawings

Cite this