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

Institute of Software Technology (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

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 $20n-2819 leq r_n leq 10n7 + 11$.

Original language	English
Title of host publication	Proc. XVIII Encuentros de Geometría Computacional
Place of Publication	Girona, Spain
Pages	43-46
Number of pages	4
Publication status	Published - 2019

Access to Document

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

Cite this

@inproceedings{53492f2501324a3d8cb2c433c6610c22,

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",

year = "2019",

language = "English",

pages = "43--46",

booktitle = "Proc. XVIII Encuentros de Geometr{\'i}a Computacional",

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TY - GEN

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 -