Leonardo Martínez-Sandoval

activity

20152020

most citedA geometric Hall-type theorem

3 citations · 8 across the 6 of their papers we have counts for

collaborators

9 papers

cs.CG2020

Rainbow polygons for colored point sets in the plane

David Flores-Peñaloza, Mikio Kano, Leonardo Martínez-Sandoval +5

Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let…

math.CO2019★ 2 cited

The convex dimension of hypergraphs and the hypersimplicial Van Kampen-Flores Theorem

Leonardo Martínez-Sandoval, Arnau Padrol

The convex dimension of a $k$ -uniform hypergraph is the smallest dimension $d$ for which there is an injective mapping of its vertices into $R^{d}$ such that the set of $k$ -…

math.CO2018

Further Consequences of the Colorful Helly Hypothesis

Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado, Natan Rubin

Let $F$ be a family of convex sets in $R^{d}$ , which are colored with $d + 1$ colors. We say that $F$ satisfies the Colorful Helly Property if every rainb…

math.CO2017

On lattice path matroid polytopes: integer points and Ehrhart polynomial

Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín

In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the…

cs.CG2017★ 1 cited

Bounding a global red-blue proportion using local conditions

Márton Naszódi, Leonardo Martínez-Sandoval, Shakhar Smorodinsky

We study the following local-to-global phenomenon: Let $B$ and $R$ be two finite sets of (blue and red) points in the Euclidean plane $R^{2}$ . Suppose that in each "neighbor…

math.CO2016

Codimension two and three Kneser Transversals

Jonathan Chappelon, Leonardo Martínez-Sandoval, Luis Montejano +2

Let $k, d, λ ⩾ 1$ be integers with $d ⩾ λ$ and let $X$ be a finite set of points in $R^{d}$ . A $(d - λ)$ -plane $L$ transversal to the convex hulls of all $k$ -set…

math.CO2015★ 2 cited

Complete Kneser Transversals

Jonathan Chappelon, Leonardo Martínez-Sandoval, Luis Montejano +2

Let $k, d, λ ⩾ 1$ be integers with $d ⩾ λ$ . Let $m (k, d, λ)$ be the maximum positive integer $n$ such that every set of $n$ points (not necessarily in general position) in…

math.CO2015

A Tutte polynomial inequality for lattice path matroids

Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín

Let $M$ be a matroid without loops or coloops and let $T (M; x, y)$ be its Tutte polynomial. In 1999 Merino and Welsh conjectured that $max (T (M; 2, 0), T (M; 0, 2)) \geq T (M; 1, 1)$ holds…

math.CO2015★ 3 cited

A geometric Hall-type theorem

Andreas Holmsen, Leonardo Martinez-Sandoval, Luis Montejano

We introduce a geometric generalization of Hall's marriage theorem. For any family $F = {X_{1}, \dots, X_{m}}$ of finite sets in $R^{d}$ , we give conditions under which it is…