eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-19
270
281
10.4230/LIPIcs.IPEC.2015.270
article
A Polynomial Kernel for Block Graph Deletion
Kim, Eun Jung
Kwon, O-joung
In the Block Graph Deletion problem, we are given a graph G on n vertices and a positive integer k, and the objective is to check whether it is possible to delete at most k vertices from G to make it a block graph, i.e., a graph in which each block is a clique. In this paper, we obtain a kernel with O(k^{6}) vertices for the Block Graph Deletion problem. This is a first step to investigate polynomial kernels for deletion problems into non-trivial classes of graphs of bounded rank-width, but unbounded tree-width. Our result also implies that Chordal Vertex Deletion admits a polynomial-size kernel on diamond-free graphs. For the kernelization and its analysis, we introduce the notion of 'complete degree' of a vertex. We believe that the underlying idea can be potentially applied to other problems. We also prove that the Block Graph Deletion problem can be solved in time 10^{k} * n^{O(1)}.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol043-ipec2015/LIPIcs.IPEC.2015.270/LIPIcs.IPEC.2015.270.pdf
block graph
polynomial kernel
single-exponential FPT algorithm