The MULTICUT IN TREES problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer k, whether there exists a set of k edges cutting all the requests. This problem was shown to be FPT by Guo and Niedermeyer. They also provided an exponential kernel. They asked whether this problem has a polynomial kernel. This question was also raised by Fellows. We show that MULTICUT IN TREES has a polynomial kernel.
@article{arxiv.0902.1047,
title = {A Polynomial Kernel For Multicut In Trees},
author = {Nicolas Bousquet and Jean Daligault and Stephan Thomasse and Anders Yeo},
journal= {arXiv preprint arXiv:0902.1047},
year = {2009}
}