Perfect rainbow polygons for colored point sets in the plane

David Flores-Peñaloza; Mikio Kano; Leonardo Martínez-Sandoval; David Orden; Javier Tejel; Csaba D. Tóth; Jorge Urrutia; Birgit Vogtenhuber

Perfect rainbow polygons for colored point sets in the plane

David Flores-Peñaloza, Mikio Kano, Leonardo Martínez-Sandoval, David Orden, Javier Tejel, Csaba D. Tóth, Jorge Urrutia, Birgit Vogtenhuber

Institut für Softwaretechnologie (7160)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

Abstract

Given a planar $n$-colored point set $S= S_1 cup ldots cup S_n$ in general position, a simple polygon $P$ is called a perfect rainbow polygon if it contains exactly one point of each color. The rainbow index $r_n$ is the minimum integer $m$ such that every $n$-colored point set $S$ has a perfect rainbow polygon with at most $m$ vertices. We determine the values of $r_n$ for $n leq 7$, and prove that in general $20n-2819 leq r_n leq 10n7 + 11$.

Originalsprache	englisch
Titel	Proc. XVIII Encuentros de Geometría Computacional
Erscheinungsort	Girona, Spain
Seiten	43-46
Seitenumfang	4
Publikationsstatus	Veröffentlicht - 2019

Zugriff auf Dokument

http://imae.udg.edu/egc2019/doc/BookAbstractsEGC2019.pdf

Dieses zitieren

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title = "Perfect rainbow polygons for colored point sets in the plane",

abstract = "Given a planar $n$-colored point set $S= S_1 cup ldots cup S_n$ in general position, a simple polygon $P$ is called a perfect rainbow polygon if it contains exactly one point of each color. The rainbow index $r_n$ is the minimum integer $m$ such that every $n$-colored point set $S$ has a perfect rainbow polygon with at most $m$ vertices. We determine the values of $r_n$ for $n leq 7$, and prove that in general $20n-2819 leq r_n leq 10n7 + 11$.",

author = "David Flores-Pe{\~n}aloza and Mikio Kano and Leonardo Mart{\'i}nez-Sandoval and David Orden and Javier Tejel and T{\'o}th, {Csaba D.} and Jorge Urrutia and Birgit Vogtenhuber",

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T1 - Perfect rainbow polygons for colored point sets in the plane

AU - Flores-Peñaloza, David

AU - Kano, Mikio

AU - Martínez-Sandoval, Leonardo

AU - Orden, David

AU - Tejel, Javier

AU - Tóth, Csaba D.

AU - Urrutia, Jorge

AU - Vogtenhuber, Birgit

PY - 2019

Y1 - 2019

N2 - Given a planar $n$-colored point set $S= S_1 cup ldots cup S_n$ in general position, a simple polygon $P$ is called a perfect rainbow polygon if it contains exactly one point of each color. The rainbow index $r_n$ is the minimum integer $m$ such that every $n$-colored point set $S$ has a perfect rainbow polygon with at most $m$ vertices. We determine the values of $r_n$ for $n leq 7$, and prove that in general $20n-2819 leq r_n leq 10n7 + 11$.

AB - Given a planar $n$-colored point set $S= S_1 cup ldots cup S_n$ in general position, a simple polygon $P$ is called a perfect rainbow polygon if it contains exactly one point of each color. The rainbow index $r_n$ is the minimum integer $m$ such that every $n$-colored point set $S$ has a perfect rainbow polygon with at most $m$ vertices. We determine the values of $r_n$ for $n leq 7$, and prove that in general $20n-2819 leq r_n leq 10n7 + 11$.

M3 - Conference paper

SP - 43

EP - 46

BT - Proc. XVIII Encuentros de Geometría Computacional

CY - Girona, Spain

ER -