A Linear Vertex Kernel for Maximum Internal Spanning Tree
Data Structures and Algorithms
2012-03-06 v2 Discrete Mathematics
Abstract
We 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' 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."
Cite
@article{arxiv.0907.3208,
title = {A Linear Vertex Kernel for Maximum Internal Spanning Tree},
author = {Fedor V. Fomin and Serge Gaspers and Saket Saurabh and Stéphan Thomassé},
journal= {arXiv preprint arXiv:0907.3208},
year = {2012}
}