Dominating sets in planar graphs

Lesley R. Matheson, Robert E. Tarjan

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

Motivated by an application to unstructured multigrid calculations, we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs. Specifically, we wish to find the smallest ε such that, for n sufficiently large, every n-vertex planar graph contains a dominating set of size at most εn. We prove that 1/4 ≤s ε ≤ 1/3, and we conjecture that ε = 1/4. For triangulated discs we obtain a tight bound of ε = 1/3. The upper bound proof yields a linear-time algorithm for finding an (n/3)-size dominating set.

Original languageEnglish (US)
Pages (from-to)565-568
Number of pages4
JournalEuropean Journal of Combinatorics
Volume17
Issue number6
DOIs
StatePublished - Aug 1996

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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