Triangle-free graphs with large independent domination number

Wai Chee SHIU*, Xue gang Chen, Wai Hong Chan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Let G be a simple graph of order n and minimum degree δ. The independent domination number i (G) is defined as the minimum cardinality of an independent dominating set of G. We prove the following conjecture due to Haviland [J. Haviland, Independent domination in triangle-free graphs, Discrete Mathematics 308 (2008), 3545-3550]: If G is a triangle-free graph of order n and minimum degree δ, then i (G) ≤ n - 2 δ for n / 4 ≤ δ ≤ n / 3, while i (G) ≤ δ for n / 3 < δ ≤ 2 n / 5. Moreover, the extremal graphs achieving these upper bounds are also characterized.

Original languageEnglish
Pages (from-to)86-92
Number of pages7
JournalDiscrete Optimization
Volume7
Issue number1-2
DOIs
Publication statusPublished - Feb 2010

Scopus Subject Areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Independent domination number
  • Triangle-free graphs

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