Artículo
Cover contact graphs
Autor/es | Atienza Martínez, María Nieves
Castro Ochoa, Natalia de Cortés Parejo, María del Carmen Garrido Vizuete, María de los Angeles Grima Ruiz, Clara Isabel Hernández, Gregorio Márquez Pérez, Alberto Moreno González, Auxiliadora Nöllenburg, Martin Portillo Fernández, José Ramón Reyes Colume, Pedro Valenzuela Muñoz, Jesús Villar Liñán, María Trinidad Wolff, Alexander |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2012 |
Fecha de depósito | 2016-03-17 |
Publicado en |
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Resumen | We study problems that arise in the context of covering certain geometric
objects called seeds (e.g., points or disks) by a set of other geometric objects called cover
(e.g., a set of disks or homothetic triangles). We ... We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by a set of other geometric objects called cover (e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, respectively, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in three types of tasks, both in the general case and in the special case of seeds on a line: (a) deciding whether a given seed set has a connected CCG, (b) deciding whether a given graph has a realization as a CCG on a given seed set, and (c) bounding the sizes of certain classes of CCG’s. Concerning (a) we give efficient algorithms for the case that seeds are points and show that the problem becomes hard if seeds and covers are disks. Concerning (b) we show that this problem is hard even for point seeds and disk covers (given a fixed correspondence between graph vertices and seeds). Concerning (c) we obtain upper and lower bounds on the number of CCG’s for point seeds. |
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