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Triangle-free graphs with large independent domination number

被引：8
|
作者：
Shiu, Wai Chee [1 ]
Chen, Xue-gang [2 ]
Chan, Wai Hong [1 ]
机构：
[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
[2] N China Elect Power Univ, Dept Math, Beijing 102206, Peoples R China
来源：
DISCRETE OPTIMIZATION | 2010年 / 7卷 / 1-2期
关键词：
Independent domination number; Triangle-free graphs;
D O I：
10.1016/j.disopt.2010.02.004
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
Let G be a simple graph of order n and minimum degree delta. 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 delta, then i(G) <= n - 2 delta for n/4 <= delta <= n/3, while i(G) <= delta for n/3 < delta <= 2n/5. Moreover, the extremal graphs achieving these upper bounds are also characterized. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：86 / 92
页数：7
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