Abstract
AbstractWe present a polynomial time algorithm that for any graph G and integer k ≥ 0, either finds a spanning tree with at least k internal vertices, or outputs a new graph G R 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 R 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.”KeywordsPolynomial TimeSpan TreeBipartite GraphNonempty SubsetPolynomial Time AlgorithmThese 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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