Unit disk visibility graphs

• Deniz Agaoglu Çagırıcı ^[1] ; Onur Çagırıcı ^[2]
  1. [1] Masaryk University

     Masaryk University

     Chequia

     
  2. [2] Toronto Metropolitan University (formerly, Ryerson University), Toronto, Canada
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 17-23
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study unit disk visibility graphs, where the visibility relation between a pair ofgeometric entities is defined by not only obstacles, but also the distance between them.This particular graph class models real world scenarios more accurately compared to theconventional visibility graphs. We first define and classify the unit disk visibility graphs,and then show that the 3-coloring problem is NP-complete when unit disk visibility modelis used for a set of line segments (which applies to a set of points) even when every segmentis axis-parallel (i.e., parallel to either x- or y-axis) or when every segment has unit length(i.e., 1-unit long), and for a polygon with holes.