首页    期刊浏览 2024年12月12日 星期四
登录注册

文章基本信息

  • 标题:Conflict-Free Coloring of Intersection Graphs
  • 本地全文:下载
  • 作者:S{\'a}ndor P. Fekete ; Phillip Keldenich
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2017
  • 卷号:92
  • 页码:31:1-31:12
  • DOI:10.4230/LIPIcs.ISAAC.2017.31
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:A conflict-free k-coloring of a graph G=(V,E) assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs. We demonstrate that the intersection graph of n geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in \Omega(log n/log log n) and in \Omega(\sqrt{\log n}) for disks or squares of different sizes; it is known for general graphs that the worst case is in \Theta(log^2 n). For unit-disk intersection graphs, we prove that it is NP-complete to decide the existence of a conflict-free coloring with one color; we also show that six colors always suffice, using an algorithm that colors unit disk graphs of restricted height with two colors. We conjecture that four colors are sufficient, which we prove for unit squares instead of unit disks. For interval graphs, we establish a tight worst-case bound of two.
  • 关键词:conflict-free coloring; intersection graphs; unit disk graphs; complexity; worst-case bounds
国家哲学社会科学文献中心版权所有