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A 2lk Kernel for l-Component Order Connectivity

Authors Mithilesh Kumar, Daniel Lokshtanov

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Mithilesh Kumar
Daniel Lokshtanov

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Mithilesh Kumar and Daniel Lokshtanov. A 2lk Kernel for l-Component Order Connectivity. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.IPEC.2016.20

Abstract

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.
Keywords
  • Parameterized algorithms
  • Kernel
  • Component Order Connectivity
  • Max-min allocation
  • Weighted expansion

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