On the maximum number of minimum dominating sets in forests

被引：14
|
作者：
Alvarado, J. D. [1 ]
Dantas, S. [1 ]
Mohr, E. [2 ]
Rautenbach, D. [2 ]
机构：
[1] Univ Fed Fluminense, Inst Matemat & Estat, Niteroi, RJ, Brazil
[2] Univ Ulm, Inst Optimierung & Operat Res, Ulm, Germany
来源：
DISCRETE MATHEMATICS | 2019年 / 342卷 / 04期
关键词：
Tree; Domination number; Minimum dominating set; Independence number; Maximum independent set; INDEPENDENT SETS; EXTREMAL NUMBERS; TREES;
D O I：
10.1016/j.disc.2018.11.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number gamma has at most 2(gamma) minimum dominating sets. Bien gave a counterexample, which allows us to construct forests with domination number gamma and 2.0598(gamma) minimum dominating sets. We show that every forest with domination number gamma has at most 2.4606(gamma) minimum dominating sets, and that every tree with independence number alpha has at most 2(alpha-1) + 1 maximum independent sets. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：934 / 942
页数：9
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