http://dx.doi.org/10.1016/j.disopt.2010.02.004">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Triangle-free graphs with large independent domination number

Language

English

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. © 2010 Elsevier B.V. All rights reserved.

Keywords

Independent domination number, Triangle-free graphs

Publication Date

2010

Source Publication Title

Discrete Optimization

Volume

7

Issue

2-1

Start Page

86

End Page

92

Publisher

Elsevier

ISSN (print)

15725286

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