Complete Geometric Graphs with no Partition into Plane Spanning Trees

Johannes Obenaus; Joachim Orthaber

Complete Geometric Graphs with no Partition into Plane Spanning Trees

Johannes Obenaus
, Joachim Orthaber

Institute of Software Engineering and Artificial Intelligence (7160)

Research output: Contribution to conference › Abstract

Abstract

It is a long-standing conjecture that every complete geometric graph on 2n vertices can be partitioned into n plane spanning trees. Despite several approaches, it remained open to this day. In this note we provide a family of counterexamples, based on bumpy wheel sets.

Original language	English
Pages	38-39
Number of pages	2
Publication status	Published - Sept 2021
Event	23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games - Chiang Mai, Thailand Duration: 3 Sept 2021 → 5 Sept 2021 https://www.math.science.cmu.ac.th/tjcdcggg/

Conference

Conference	23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games
Abbreviated title	TJCDCG^3 2020+1
Country/Territory	Thailand
City	Chiang Mai
Period	3/09/21 → 5/09/21
Internet address	https://www.math.science.cmu.ac.th/tjcdcggg/

Fields of Expertise

Information, Communication & Computing

Access to Document

https://www.math.science.cmu.ac.th/tjcdcggg/Book-abstract.pdf

1 Workshop, seminar or course (Participation in/Organisation of)

5th DACH Workshop on Arrangements and Drawings
Orthaber, J. (Participant)
16 Mar 2021 → 23 Mar 2021
Activity: Participation in or organisation of › Workshop, seminar or course (Participation in/Organisation of)

1 Preprint

Edge Partitions of Complete Geometric Graphs (Part 1)
Obenaus, J. & Orthaber, J., 11 Aug 2021.
Research output: Working paper › Preprint

Cite this

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title = "Complete Geometric Graphs with no Partition into Plane Spanning Trees",

abstract = "It is a long-standing conjecture that every complete geometric graph on 2n vertices can be partitioned into n plane spanning trees. Despite several approaches, it remained open to this day. In this note we provide a family of counterexamples, based on bumpy wheel sets.",

author = "Johannes Obenaus and Joachim Orthaber",

year = "2021",

month = sep,

language = "English",

pages = "38--39",

note = "23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games, TJCDCG\textasciicircum{}3 2020+1 ; Conference date: 03-09-2021 Through 05-09-2021",

url = "https://www.math.science.cmu.ac.th/tjcdcggg/",

}

TY - CONF

T1 - Complete Geometric Graphs with no Partition into Plane Spanning Trees

AU - Obenaus, Johannes

AU - Orthaber, Joachim

PY - 2021/9

Y1 - 2021/9

N2 - It is a long-standing conjecture that every complete geometric graph on 2n vertices can be partitioned into n plane spanning trees. Despite several approaches, it remained open to this day. In this note we provide a family of counterexamples, based on bumpy wheel sets.

AB - It is a long-standing conjecture that every complete geometric graph on 2n vertices can be partitioned into n plane spanning trees. Despite several approaches, it remained open to this day. In this note we provide a family of counterexamples, based on bumpy wheel sets.

M3 - Abstract

SP - 38

EP - 39

T2 - 23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games

Y2 - 3 September 2021 through 5 September 2021

ER -

Complete Geometric Graphs with no Partition into Plane Spanning Trees

Abstract

Conference

Fields of Expertise

Access to Document

Activities

5th DACH Workshop on Arrangements and Drawings

Research output

Edge Partitions of Complete Geometric Graphs (Part 1)

Cite this