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Kernelization for Maximum Leaf Spanning Tree with Positive Vertex Weights

  • Bart Jansen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)

Abstract

In this paper we consider a natural generalization of the well-known Max Leaf Spanning Tree problem. In the generalized Weighted Max Leaf problem we get as input an undirected connected graph G = (V,E), a rational number k ≥ 1 and a weight function \(w: V \longmapsto Q_{\geq 1}\) on the vertices, and are asked whether a spanning tree T for G exists such that the combined weight of the leaves of T is at least k. We show that it is possible to transform an instance 〈G,w, k 〉 of Weighted Max Leaf in linear time into an equivalent instance 〈G′,w′, k′ 〉 such that |V′| ≤ 5.5k′ and k′ ≤ k. In the context of fixed parameter complexity this means that Weighted Max Leaf admits a kernel with 5.5k vertices. The analysis of the kernel size is based on a new extremal result which shows that every graph G that excludes some simple substructures always contains a spanning tree with at least |V|/5.5 leaves.

Keywords

Span Tree Vertex Cover Reduction Rule Leaf Weight Dead Leaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bart Jansen
    • 1
  1. 1.Utrecht UniversityUtrechtThe Netherlands

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