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Your search keyword '"Garcia-Colin, N' showing total 4 results
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4 results on '"Garcia-Colin, N'

1. Geometric achromatic and pseudoachromatic indices

Author

Aichholzer, O., Araujo-Pardo, G., García-Colín, N., Hackl, T., Lara, D., Rubio-Montiel, C., and Urrutia, J.

Subjects
Mathematics - Combinatorics
Abstract

The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn in the plane such that its vertices are points in general position, and its edges are straight-line segments. In this paper we extend the notion of pseudoachromatic and achromatic indices for geometric graphs, and present results for complete geometric graphs. In particular, we show that for $n$ points in convex position the achromatic index and the pseudoachromatic index of the complete geometric graph are $\lfloor \tfrac{n^2+n}{4} \rfloor$., Comment: 21 pages, 10 figures

Published
2013
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2. On the number of vertices of projective polytopes

Author

Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Garcia-Colin, N; Montejano, LP; Alfonsin, JLR, Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, and Garcia-Colin, N; Montejano, LP; Alfonsin, JLR

Abstract

Let X be a set of n points in Rd$\mathbb {R}<^>d$ in general position. What is the maximum number of vertices that conv(T(X))$\mathsf {conv}(T(X))$ can have among all the possible permissible projective transformations T? In this paper, we investigate this and other related questions. After presenting several upper bounds, obtained by using oriented matroid machinery, we study a closely related problem (via Gale transforms) concerning the maximal number of minimal Radon partitions of a set of points. The latter led us to a result supporting a positive answer to a question of Pach and Szegedy asking whether balanced 2-colorings of points in the plane maximize the number of induced multicolored Radon partitions. We also discuss a related problem concerning the size of topes in arrangements of hyperplanes as well as a tolerance-type problem of finite sets.

Published
2023

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