Projects per year
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 |
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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 | |
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 |
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Volume | 224 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 38th International Symposium on Computational Geometry |
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Abbreviated title | SoCG 2022 |
Country/Territory | Germany |
City | Berlin |
Period | 7/06/22 → 10/06/22 |
Internet address |
Keywords
- complete geometric graph
- edge partition
- plane spanning tree
- wheel set
ASJC Scopus subject areas
- Software
Fields of Expertise
- Information, Communication & Computing
Fingerprint
Dive into the research topics of 'Edge Partitions of Complete Geometric Graphs'. Together they form a unique fingerprint.Projects
- 1 Active
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Doctoral Program: Discrete Mathematics
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
Project: Research project
Activities
- 1 Workshop, seminar or course (Participation in/Organisation of)
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5th DACH Workshop on Arrangements and Drawings
Joachim Orthaber (Participant)
16 Mar 2021 → 23 Mar 2021Activity: Participation in or organisation of › Workshop, seminar or course (Participation in/Organisation of)