2015/09/05 by Marthe Bonamy, Łukasz Kowalik, Bonamy, Marthe +5
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1509.01675
Extended abstract accepted for IPEC'15, 27 pages
arxiv created 2015/09/05 · arxiv updated 2015/09/08
In the k-Leaf Out-Branching and k-Internal Out-Branching problems we are given a directed graph D with a designated root r and a nonnegative integer k. The question is to determine the existence of an outbranching rooted at r that has at least k leaves, or at least k internal vertices, respectively. Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k2) vertices are known on general graphs. In this work we show that k-Leaf Out-Branching admits a kernel with O(k) vertices on H-minor-free graphs, for any fixed family of graphs H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices on any graph class of bounded expansion.