Disjoint Compatibility via Graph Classes

Oswin Aichholzer, Julia Obmann, Pavel Paták, Daniel Perz*, Josef Tkadlec, Birgit Vogtenhuber

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


Two plane drawings of 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. Let S be a convex point set of $$2n \ge 10$$ points and let $$\mathcal {H}$$ be a family of plane drawings on S. Two plane perfect matchings $$M:1$$ and $$M:2$$ on S (which do not need to be disjoint nor compatible) are disjoint $$\mathcal {H}$$ -compatible if there exists a drawing in $$\mathcal {H}$$ which is disjoint compatible to both $$M:1$$ and $$M:2$$. In this work, we consider the graph which has all plane perfect matchings as vertices and where two vertices are connected by an edge if the matchings are disjoint $$\mathcal {H}$$ -compatible. We study the diameter of this graph when $$\mathcal {H}$$ is the family of all plane spanning trees, caterpillars or paths. We show that in the first two cases the graph is connected with constant and linear diameter, respectively, while in the third case it is disconnected.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 48th International Workshop, WG 2022, Revised Selected Papers
EditorsMichael A. Bekos, Michael Kaufmann
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783031159138
Publication statusPublished - 2022
Event48th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2022 - Tübingen, Germany
Duration: 22 Jun 202224 Jun 2022

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference48th International Workshop on Graph-Theoretic Concepts in Computer Science
Abbreviated titleWG 2022


  • Compatibility
  • Convex Set
  • Matchings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fields of Expertise

  • Information, Communication & Computing


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