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 language | English |
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Pages (from-to) | 86-92 |
Number of pages | 7 |
Journal | Discrete Optimization |
Volume | 7 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Feb 2010 |
User-Defined Keywords
- Independent domination number
- Triangle-free graphs