Výsledky vyhledávání - "Aguilar, Hernán A."

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Autor: González-Aguilar, Hernán, Orden, David, Pérez-Lantero, Pablo, Rappaport, David, Seara, Carlos, Tejel, Javier, Urrutia, Jorge

Publikováno v: SIAM Journal on Computing 50(1) (2021), 145-170

Let $P$ be a set of $n$ points in the plane. We consider a variation of the classical Erd\H{o}s-Szekeres problem, presenting efficient algorithms with $O(n^3)$ running time and $O(n^2)$ space complexity that compute: (1) A subset $S$ of $P$ such that

Externí odkaz: http://arxiv.org/abs/1907.07441

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The complexity of computing the cylindrical and the $t$-circle crossing number of a graph

Autor: Duque, Frank, González-Aguilar, Hernán, Hernández-Vélez, César, Leaños, Jesús, Medina, Carolina

Publikováno v: Electron. J. Combin. 25 (2018), no. 2, Paper 2.43, 11 pp

A plane drawing of a graph is {\em cylindrical} if there exist two concentric circles that contain all the vertices of the graph, and no edge intersects (other than at its endpoints) any of these circles. The {\em cylindrical crossing number} of a gr

Externí odkaz: http://arxiv.org/abs/1708.01942

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On $k$-Gons and $k$-Holes in Point Sets

Autor: Aichholzer, Oswin, Fabila-Monroy, Ruy, González-Aguilar, Hernán, Hackl, Thomas, Heredia, Marco A., Huemer, Clemens, Urrutia, Jorge, Valtr, Pavel, Vogtenhuber, Birgit

We consider a variation of the classical Erd\H{o}s-Szekeres problems on the existence and number of convex $k$-gons and $k$-holes (empty $k$-gons) in a set of $n$ points in the plane. Allowing the $k$-gons to be non-convex, we show bounds and structu

Externí odkaz: http://arxiv.org/abs/1409.0081

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Large convex holes in random point sets

Autor: Balogh, József, González-Aguilar, Hernán, Salazar, Gelasio

A {\em convex hole} (or {\em empty convex polygon)} of a point set $P$ in the plane is a convex polygon with vertices in $P$, containing no points of $P$ in its interior. Let $R$ be a bounded convex region in the plane. We show that the expected numb

Externí odkaz: http://arxiv.org/abs/1206.0805

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On the Connectedness and Diameter of a Geometric Johnson Graph

Autor: Bautista-Santiago, Crevel, Cano, Javier, Fabila-Monroy, Ruy, Flores-Peñaloza, David, González-Aguilar, Hernán, Lara, Dolores, Sarmiento, Eliseo, Urrutia, Jorge

Let $P$ be a set of $n$ points in general position in the plane. A subset $I$ of $P$ is called an \emph{island} if there exists a convex set $C$ such that $I = P \cap C$. In this paper we define the \emph{generalized island Johnson graph} of $P$ as t

Externí odkaz: http://arxiv.org/abs/1202.3455

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