A linear vertex kernel for maximum internal spanning tree

Fedor V. Fomin, Serge Gaspers, Saket Saurabh, Stéphan Thomassé
2013 Journal of computer and system sciences (Print)  
We present a polynomial time algorithm that for any graph G and integer k ≥ 0, either nds a spanning tree with at least k internal vertices, or outputs a new graph GR 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 GR 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
more » ... sult 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.
doi:10.1016/j.jcss.2012.03.004 fatcat:payufjicgrewbgoray25pw6wqi