Unit disk graphs

Brent N. Clark, Charles J. Colbourn, David S. Johnson

Research output: Contribution to journalArticle

952 Scopus citations

Abstract

Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.

Original languageEnglish (US)
Pages (from-to)165-177
Number of pages13
JournalDiscrete Mathematics
Volume86
Issue number1-3
DOIs
StatePublished - Dec 14 1990
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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