On domination in connected cubic graphs

A. V. Kostochka, B. Y. Stodolsky

Research output: Contribution to journalArticle

Abstract

In 1996, Reed proved that the domination number γ(G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that γ(H)≤⌈n/3⌉ for every connected 3-regular (cubic) n-vertex graph H. In this note, we disprove this conjecture. We construct a connected cubic graph G on 60 vertices with γ(G)=21 and present a sequence ⌈Gk⌉k=1∞ of connected cubic graphs withlimk→∞γ(Gk)|V(Gk)|≥823=13+169.

Original languageEnglish (US)
Pages (from-to)45-50
Number of pages6
JournalDiscrete Mathematics
Volume304
Issue number1-3
DOIs
StatePublished - Nov 28 2005

Keywords

  • Cubic graphs
  • Dominating set
  • Domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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