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

页码：86 / 92

页数：7

共 50 条

[31] Independent dominating sets in triangle-free graphs
Goddard, Wayne
Lyle, Jeremy
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2012, 23 (01) : 9 - 20
[32] On the cycle isolation number of triangle-free graphs
Zhang, Gang
Wu, Baoyindureng
DISCRETE MATHEMATICS, 2024, 347 (12)
[33] Neighborhood Total Domination and Maximum Degree in Triangle-Free Graphs
Henning, Michael A.
Mojdeh, D. A.
Salehi, M. R. Sayed
UTILITAS MATHEMATICA, 2018, 107 : 137 - 150
[34] Triangle-free graphs with large chromatic numbers
Nilli, A
DISCRETE MATHEMATICS, 2000, 211 (1-3) : 261 - 262
[35] Triangle-free planar graphs with small independence number
Dvorak, Zdenek
Venters, Jordan
EUROPEAN JOURNAL OF COMBINATORICS, 2019, 76 : 88 - 103
[36] Triangle-free planar graphs with the smallest independence number
Dvorak, Zdenek
Masarik, Tomas
Musilek, Jan
Pangrac, Ondrej
JOURNAL OF GRAPH THEORY, 2019, 90 (03) : 443 - 454
[37] The fractional chromatic number of triangle-free graphs with Δ ≤ 3
Lu, Linyuan
Peng, Xing
DISCRETE MATHEMATICS, 2012, 312 (24) : 3502 - 3516
[38] Circular chromatic number of triangle-free hexagonal graphs
Sparl, Petra
Zerovnik, Janez
SOR'07: PROCEEDINGS OF THE 9TH INTERNATIONAL SYMPOSIUM ON OPERATIONAL RESEARCH IN SLOVENIA, 2007, : 75 - 79
[39] ON THE AVERAGE SIZE OF INDEPENDENT SETS IN TRIANGLE-FREE GRAPHS
Davies, Ewan
Jenssen, Matthew
Perkins, Will
Roberts, Barnaby
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (01) : 111 - 124
[40] On vertex orderings and the stability number in triangle-free graphs
Rautenbach, D
DISCRETE MATHEMATICS, 2001, 231 (1-3) : 411 - 420

← 1 2 3 4 5 →