A Linear Vertex Kernel for Maximum Internal Spanning Tree

Fedor V. Fomin 1 Serge Gaspers 2 Saket Saurabh 1 Stéphan Thomassé 2
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We present a polynomial time algorithm that for any graph G and integer k either finds a spanning tree with at least k internal vertices, or outputs a new graph G' on at most 3k vertices and an integer k' such that G' has a spanning tree with at least k internal vertices if and only if G' has a spanning tree with at least k' internal vertices. In other words, we show that the Maximum Internal Spanning Tree problem parameterized by the number of internal vertices k, has a 3k-vertex kernel. Our result is based on an innovative application of a classical min-max result about hypertrees in hypergraphs which states that "a hypergraph H contains a hypertree if and only if H is partition connected."
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Conference papers
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00432674
Contributor : Serge Gaspers <>
Submitted on : Monday, November 16, 2009 - 9:10:34 PM
Last modification on : Tuesday, January 22, 2019 - 7:10:05 PM

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Fedor V. Fomin, Serge Gaspers, Saket Saurabh, Stéphan Thomassé. A Linear Vertex Kernel for Maximum Internal Spanning Tree. ISAAC'09: 20th International Symposium on Algorithms and Computation, pp.9. ⟨lirmm-00432674⟩

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