Triangle-free graphs with large independent domination number

  • Authors:

  • Wai Chee Shiu;Xue-Gang Chen;Wai Hong Chan

  • Affiliations:

  • Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China;Department of Mathematics, North China Electric Power University, Beijing 102206, China;Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China

  • Venue:
  • Discrete Optimization
  • Year:
  • 2010

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Abstract

Let G be a simple graph of order n and minimum degree @d. 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 @d, then i(G)@?n-2@d for n/4@?@d@?n/3, while i(G)@?@d for n/3