Cover contact graphs

N. Atienza, N. Castro, de, C. Cortes, M.A. Garrido, C. Grima, G. Hernandez, A. Márquez, A. Moreno, M. Nöllenburg, J.R. Portillo, P. Reyes, J. Valenzuela, M.T. Villar, A. Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)


We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-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, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).
Original languageEnglish
Title of host publicationGraph Drawing (15th International Symposium, GD'07, Sydney, Australia, September 23-26, 2007, Revised Papers)
EditorsS.K. Hong, T. Nishizeki, W. Quan
Place of PublicationBerlin
ISBN (Print)978-3-540-77536-2
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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