Disjoint tree-compatible plane perfect matchings

Oswin Aichholzer; Julia Obmann; Pavel Paták; Daniel Perz; Josef Tkadlec

Disjoint tree-compatible plane perfect matchings

Oswin Aichholzer, Julia Obmann, Pavel Paták, Daniel Perz, Josef Tkadlec

Institute of Software Technology (7160)

Research output: Contribution to conference › Paper › peer-review

Abstract

Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two
plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is
disjoint compatible to both M1 and M2.
We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter
of this graph is either 4 or 5, independent of n.

Original language	English
Pages	56:1
Publication status	Published - 2020
Event	36th European Workshop on Computational Geometry - University of Würzburg, Virtuell, Germany Duration: 16 Mar 2020 → 18 Mar 2020 https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/

Conference

Conference	36th European Workshop on Computational Geometry
Abbreviated title	EuroCG 2020
Country/Territory	Germany
City	Virtuell
Period	16/03/20 → 18/03/20
Internet address	https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/

Access to Document

https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_56.pdf

1 Conference or symposium (Participation in/Organisation of)

36th European Workshop on Computational Geometry
Daniel Perz (Participant)
16 Mar 2020 → 18 Mar 2020
Activity: Participation in or organisation of › Conference or symposium (Participation in/Organisation of)

Cite this

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title = "Disjoint tree-compatible plane perfect matchings",

abstract = "Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points twoplane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which isdisjoint compatible to both M1 and M2.We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameterof this graph is either 4 or 5, independent of n.",

author = "Oswin Aichholzer and Julia Obmann and Pavel Pat{\'a}k and Daniel Perz and Josef Tkadlec",

year = "2020",

language = "English",

pages = "56:1",

note = "36th European Workshop on Computational Geometry , EuroCG 2020 ; Conference date: 16-03-2020 Through 18-03-2020",

url = "https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/",

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T1 - Disjoint tree-compatible plane perfect matchings

AU - Aichholzer, Oswin

AU - Obmann, Julia

AU - Paták, Pavel

AU - Perz, Daniel

AU - Tkadlec, Josef

PY - 2020

Y1 - 2020

N2 - Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points twoplane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which isdisjoint compatible to both M1 and M2.We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameterof this graph is either 4 or 5, independent of n.

AB - Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points twoplane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which isdisjoint compatible to both M1 and M2.We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameterof this graph is either 4 or 5, independent of n.

M3 - Paper

SP - 56:1

T2 - 36th European Workshop on Computational Geometry

Y2 - 16 March 2020 through 18 March 2020

ER -

Disjoint tree-compatible plane perfect matchings

Abstract

Conference

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Activities

36th European Workshop on Computational Geometry

Cite this