Transition operations over plane trees

Torrie L. Nichols, Alexander Pilz, Csaba D. Tóth, Ahad N. Zehmakan

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

Abstract

The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and geometric graphs. For the latter, several variants have been studied (e.g., edge slides and edge rotations). In a transition graph on the set T(S) of noncrossing straight-line spanning trees on a finite point set S in the plane, two spanning trees are connected by an edge if one can be transformed into the other by such an operation. We study bounds on the diameter of these graphs, and consider the various operations both on general point sets and sets in convex position. In addition, we address the problem variant where operations may be performed simultaneously. We prove new lower and upper bounds for the diameters of the corresponding transition graphs and pose open problems.

Original languageEnglish
Title of host publicationLATIN 2018
Subtitle of host publicationTheoretical Informatics - 13th Latin American Symposium, Proceedings
PublisherSpringer Verlag Heidelberg
Pages835-848
Number of pages14
ISBN (Print)9783319774039
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes
Event13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina
Duration: 16 Apr 201819 Apr 2018

Publication series

NameLecture Notes in Computer Science
Volume10807
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Symposium on Latin American Theoretical Informatics, LATIN 2018
CountryArgentina
CityBuenos Aires
Period16/04/1819/04/18

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Nichols, T. L., Pilz, A., Tóth, C. D., & Zehmakan, A. N. (2018). Transition operations over plane trees. In LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings (pp. 835-848). (Lecture Notes in Computer Science; Vol. 10807 ). Springer Verlag Heidelberg. https://doi.org/10.1007/978-3-319-77404-6_60