2010/10/07 by Fomin, Fedor V., Lokshtanov, Daniel, Misra, Neeldhara +2 · 2 citations
#Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1010.1365
We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most k vertices can be deleted from a graph G such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the F-deletion problem when F contains a planar graph. We give (1) a linear vertex kernel on graphs excluding t-claw K1,t, the star with t leves, as an induced subgraph, where t is a fixed integer. (2) an approximation algorithm achieving an approximation ratio of O(log3/2 OPT), where OPT is the size of an optimal solution on general undirected graphs. Finally, we obtain polynomial kernels for the case when F contains graph θc as a minor for a fixed integer c. The graph θc consists of two vertices connected by c parallel edges. Even though this may appear to be a very restricted class of problems it already encompasses well-studied problems such as \sc Vertex Cover, \sc Feedback Vertex Set and Diamond Hitting Set. The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.