Linear Kernels for Outbranching Problems in Sparse Digraphs
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(k^2) 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 H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices on any graph class of bounded expansion.
FPT algorithm
kernelization
outbranching
sparse graphs
199-211
Regular Paper
Marthe
Bonamy
Marthe Bonamy
Lukasz
Kowalik
Lukasz Kowalik
Michal
Pilipczuk
Michal Pilipczuk
Arkadiusz
Socala
Arkadiusz Socala
10.4230/LIPIcs.IPEC.2015.199
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