On domination in connected cubic graphs

A. V. Kostochka, B. Y. Stodolsky

Research output: Contribution to journalArticlepeer-review


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
Issue number1-3
StatePublished - Nov 28 2005


  • Cubic graphs
  • Dominating set
  • Domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'On domination in connected cubic graphs'. Together they form a unique fingerprint.

Cite this