Minimal dominating sets in graph classes: Combinatorial bounds and enumeration

被引：33
|
作者：
Couturier, Jean-Francois [1 ]
Heggernes, Pinar [2 ]
van 't Hof, Pim [2 ]
Kratsch, Dieter [1 ]
机构：
[1] Univ Lorraine, LITA, F-57045 Metz 01, France
[2] Univ Bergen, Dept Informat, N-5020 Bergen, Norway
来源：
THEORETICAL COMPUTER SCIENCE | 2013年 / 487卷
关键词：
Minimal dominating sets; Enumeration algorithms; Combinatorial bounds; Graph classes; ALGORITHMS; INTERVAL;
D O I：
10.1016/j.tcs.2013.03.026
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159(n). This upper bound might not be tight, since no examples of graphs with 1.5705(n) or more minimal dominating sets are known. For several classes of graphs, we substantially improve the upper bound on the number of minimal dominating sets. At the same time, we give algorithms for enumerating all minimal dominating sets, where the running time of each algorithm is within a polynomial factor of the proved upper bound for the graph class in question. In several cases, we provide examples of graphs containing the maximum possible number of minimal dominating sets for graphs in that class, thereby showing the corresponding upper bounds to be tight. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：82 / 94
页数：13
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