eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-02-09
20:1
20:14
10.4230/LIPIcs.IPEC.2016.20
article
A 2lk Kernel for l-Component Order Connectivity
Kumar, Mithilesh
Lokshtanov, Daniel
In the l-Component Order Connectivity problem (l in N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S subseteq V(G) such that |S| <= k and the size of the largest connected component in G-S is at most l. In this paper, we give a kernel for l-Component Order Connectivity with at most 2*l*k vertices that takes n^{O(l)} time for every constant l. On the way to obtaining our kernel, we prove a generalization of the q-Expansion Lemma to weighted graphs. This generalization may be of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol063-ipec2016/LIPIcs.IPEC.2016.20/LIPIcs.IPEC.2016.20.pdf
Parameterized algorithms
Kernel
Component Order Connectivity
Max-min allocation
Weighted expansion