On domination in connected cubic graphs

Kostochka A., Stodolsky B. Y.

DISCRETE MATHEMATICS, vol.304, pp.45-50, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 304
  • Publication Date: 2005
  • Doi Number: 10.1016/j.disc.2005.07.005
  • Journal Name: DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.45-50
  • Istanbul Technical University Affiliated: No

Abstract

In 1996, Reed proved that the domination number gamma(G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that gamma(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 gamma(G) = 21 and present a sequence {G(k)}(k=1)(infinity) of connected cubic graphs with lim(k ->infinity) gamma(G(k))/vertical bar V(G(k))vertical bar >= 8/23 = 1/3 + 1/69. (c) 2005 Elsevier B.V. All rights reserved.