On distance r-dominating and 2r-independent sets in sparse graphs

被引：8
|
作者：
Dvorak, Zdenek [1 ]
机构：
[1] Charles Univ Prague, Comp Sci Inst, Malostranske Namesti 25, CR-11800 Prague, Czech Republic
来源：
JOURNAL OF GRAPH THEORY | 2019年 / 91卷 / 02期
关键词：
approximation; dominating set; independent set; weak coloring number; APPROXIMATION ALGORITHMS; EXPANSION;
D O I：
10.1002/jgt.22426
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Dvorak [European J. Combin. 34 (2013), pp. 833-840] gave a bound on the minimum size of a distance r-dominating set in terms of the maximum size of a distance 2r-independent set and generalized coloring numbers, thus obtaining a constant-factor approximation algorithm for the parameters in any class of graphs with bounded expansion. We improve and clarify this dependence using a linear programming (LP)-based argument inspired by the work of Bansal and Umboh [Inform. Process. Lett. 122 (2017), pp. 21-24].
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页码：162 / 173
页数：12
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