Rainbow cycles in flip graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419957" target="_blank" >RIV/00216208:11320/20:10419957 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=noYFAmtzud" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=noYFAmtzud</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/18M1216456" target="_blank" >10.1137/18M1216456</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rainbow cycles in flip graphs

Popis výsledku v původním jazyce

The flip graph of triangulations has as vertices all triangulations of a convex n-gon and an edge between any two triangulations that differ in exactly one edge. An r-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation appears exactly r times. This notion of a rainbow cycle extends in a natural way to other flip graphs. In this paper we investigate the existence of r-rainbow cycles for three different flip graphs on classes of geometric objects: the aforementioned flip graph of triangulations of a convex n-gon, the flip graph of plane trees on an arbitrary set of n points, and the flip graph of noncrossing perfect matchings on a set of n points in convex position. In addition, we consider two flip graphs on classes of nongeometric objects: the flip graph of permutations of {1, 2, ..., n} and the flip graph of k-element subsets of {1, 2, ..., n}. In each of the five settings, we prove the existence and nonexistence of rainbow cycles for different values of r, n, and k.

Název v anglickém jazyce

Rainbow cycles in flip graphs

Popis výsledku anglicky

The flip graph of triangulations has as vertices all triangulations of a convex n-gon and an edge between any two triangulations that differ in exactly one edge. An r-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation appears exactly r times. This notion of a rainbow cycle extends in a natural way to other flip graphs. In this paper we investigate the existence of r-rainbow cycles for three different flip graphs on classes of geometric objects: the aforementioned flip graph of triangulations of a convex n-gon, the flip graph of plane trees on an arbitrary set of n points, and the flip graph of noncrossing perfect matchings on a set of n points in convex position. In addition, we consider two flip graphs on classes of nongeometric objects: the flip graph of permutations of {1, 2, ..., n} and the flip graph of k-element subsets of {1, 2, ..., n}. In each of the five settings, we prove the existence and nonexistence of rainbow cycles for different values of r, n, and k.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA19-08554S" target="_blank" >GA19-08554S: Struktury a algoritmy ve velmi symetrických grafech</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

1-39

Kód UT WoS článku

000546886700001

EID výsledku v databázi Scopus

2-s2.0-85079770225