Skip to main content
SpringerLink
Log in

Independent dominating sets in triangle-free graphs

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

The independent domination number of a graph is the smallest cardinality of an independent set that dominates the graph. In this paper we consider the independent domination number of triangle-free graphs. We improve several of the known bounds as a function of the order and minimum degree, thereby answering conjectures of Haviland.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Harutyunyan A, Horn P, Verstraete J (2009) Independent dominating sets in graphs of girth five (submitted)

  • Haviland J (2007) Upper bounds for independent domination in regular graphs. Discrete Math 307(21):2643–2646

    Article  MATH  MathSciNet  Google Scholar 

  • Haviland J (2008a) Independent domination in triangle-free graphs. Discrete Math 308(16):3545–3550

    Article  MATH  MathSciNet  Google Scholar 

  • Haviland J (2008b) A note on independent domination in graphs of girth 5. Australas J Combin 40:301–304

    MATH  MathSciNet  Google Scholar 

  • Haviland J (2008c) A note on independent domination in graphs of girth 6. Australas J Combin 42:171–175

    MATH  MathSciNet  Google Scholar 

  • Kim JH (1995) The Ramsey number R(3,t) has order of magnitude t 2/log t. Random Structures Algorithms 7(3):173–207

    Article  MATH  MathSciNet  Google Scholar 

  • Shiu WC, Chen XG, Chan WH, (2010) Triangle-free graphs with large independent domination number. Discrete Optim 7(1–2):86–92

    Article  MathSciNet  Google Scholar 

  • Wang C (2008) The independent domination number of maximal triangle-free graphs. Australas J Combin 42:129–136

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing and Department of Mathematical Sciences, Clemson University, Clemson, SC, USA

    Wayne Goddard

  2. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS, USA

    Jeremy Lyle

Authors
  1. Wayne Goddard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeremy Lyle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeremy Lyle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goddard, W., Lyle, J. Independent dominating sets in triangle-free graphs. J Comb Optim 23, 9–20 (2012). https://doi.org/10.1007/s10878-010-9336-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-010-9336-4

Keywords

Search

Navigation