Minimum Power Dominating Sets of Random Cubic Graphs

Liying Kang, Nicholas Wormald

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We present two heuristics for finding a small power dominating set of cubic graphs. We analyze the performance of these heuristics on random cubic graphs using differential equations. In this way, we prove that the proportion of vertices in a minimum power dominating set of a random cubic graph is asymptotically almost surely at most 0.067801. We also provide a corresponding lower bound of 1/29.7 ≈ 0.03367 using known results on bisection width.

Original languageEnglish
Pages (from-to)152-171
Number of pages20
JournalJournal of Graph Theory
Volume85
Issue number1
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • power domination
  • random cubic graphs

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