Para acceder a los documentos con el texto completo, por favor, siga el siguiente enlace: http://hdl.handle.net/2117/26089

Balanced partitions of 3-colored geometric sets in the plane
Bereg, Sergey; Hurtado Díaz, Fernando Alfredo; Kano, Mikio; Korman, Matias; Lara, Dolores; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio; Urrutia Galicia, Jorge; Verbeek, Kevin
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
Let SS be a finite set of geometric objects partitioned into classes or colors . A subset S'¿SS'¿S is said to be balanced if S'S' contains the same amount of elements of SS from each of the colors. We study several problems on partitioning 33-colored sets of points and lines in the plane into two balanced subsets: (a) We prove that for every 3-colored arrangement of lines there exists a segment that intersects exactly one line of each color, and that when there are 2m2m lines of each color, there is a segment intercepting mm lines of each color. (b) Given nn red points, nn blue points and nn green points on any closed Jordan curve ¿¿, we show that for every integer kk with 0=k=n0=k=n there is a pair of disjoint intervals on ¿¿ whose union contains exactly kk points of each color. (c) Given a set SS of nn red points, nn blue points and nn green points in the integer lattice satisfying certain constraints, there exist two rays with common apex, one vertical and one horizontal, whose union splits the plane into two regions, each one containing a balanced subset of SS.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Finite element method
Colored point sets
Bipartition
Duality
Ham-sandwich theorem
Elements finits, Mètode dels
65D Numerical approximation and computational geometry
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
Artículo
         

Mostrar el registro completo del ítem

Documentos relacionados

Otros documentos del mismo autor/a

Claverol Aguas, Mercè; Garijo Royo, Delia; Korman, Matias; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
Claverol Aguas, Mercè; Garijo, Delia; Korman, Matias; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge
Bose, Prosenjit; Collette, Sébastien; Hurtado Díaz, Fernando Alfredo; Korman, Matias; Langerman, Stefan; Sacristán Adinolfi, Vera; Saumell Mendiola, Maria
Aichholzer, Oswin; Fabila-Monroy, Ruy; Hurtado Díaz, Fernando Alfredo; Pérez Lantero, Pablo; Ruiz Vargas, Andrés; Urrutia Galicia, Jorge; Vogtenhuber, Birgit