On flips in planar matchings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423563" target="_blank" >RIV/00216208:11320/20:10423563 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/978-3-030-60440-0_17" target="_blank" >https://doi.org/10.1007/978-3-030-60440-0_17</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-60440-0_17" target="_blank" >10.1007/978-3-030-60440-0_17</a>

Result language

angličtina

Original language name

On flips in planar matchings

Original language description

In this paper we investigate the structure of flip graphs on non-crossing perfect matchings in the plane. Consider all non-crossing straight-line perfect matchings on a set of 2n points that are placed equidistantly on the unit circle. The graph Hn has those matchings as vertices, and an edge between any two matchings that differ in replacing two matching edges that span an empty quadrilateral with the other two edges of the quadrilateral, provided that the quadrilateral contains the center of the unit circle. We show that the graph Hn is connected for odd n, but has exponentially many small connected components for even n, which we characterize and count via Catalan and generalized Narayana numbers. For odd n, we also prove that the diameter of Hn is linear in n. Furthermore, we determine the minimum and maximum degree of Hn for all n, and characterize and count the corresponding vertices. Our results imply the non-existence of certain rainbow cycles, and they answer several open questions and conjectures raised in a recent paper by Felsner, Kleist, Mütze, and Sering.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA19-08554S" target="_blank" >GA19-08554S: Structures and algorithms in highly symmetric graphs</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Lecture Notes in Computer Science

ISBN

978-3-030-60439-4

ISSN

0302-9743

e-ISSN

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Number of pages

13

Pages from-to

213-225

Publisher name

SPRINGER

Place of publication

Neuveden

Event location

Leeds

Event date

Jun 24, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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