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Kernelization and approximation of distance-r independent sets on nowhere dense graphs
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-01-22 , DOI: 10.1016/j.ejc.2021.103309
Michał Pilipczuk , Sebastian Siebertz

For a positive integer r, a distance-r independent set in an undirected graph G is a set IV(G) of vertices pairwise at distance greater than r, while a distance-r dominating set is a set DV(G) such that every vertex of the graph is within distance at most r from a vertex from D. We study the duality between the maximum size of a distance-2r independent set and the minimum size of a distance-r dominating set in nowhere dense graph classes, as well as the kernelization complexity of the distance-r independent set problem on these graph classes. Specifically, we prove that the distance-r independent set problem admits an almost linear kernel on every nowhere dense graph class.



中文翻译:

距离的核化和近似[R 无处密集图上的独立集

对于正整数 [R,距离-[R 无向图中的独立集 G 是一套 一世VG 成对的顶点距离大于 [R,而距离[R 主宰集是一个集 dVG 这样图形的每个顶点最多都在距离之内 [R 来自一个顶点 d。我们研究了距离的最大大小之间的对偶关系2[R 独立设置和最小距离[R 无处密集图类中的控制集,以及距离的核化复杂度[R这些图类的独立集问题。具体来说,我们证明距离-[R 独立集问题允许在每个无处密集图类上使用几乎线性的核。

更新日期:2021-01-22
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