Abstract
In this article, we consider problems on graphs of the followingform: given a graph, remove p edges/vertices to achieve some property.The first kind of problems are separation problems on undirectedgraphs, where we aim at separating distinguished vertices in an graph.The second kind of problems are feedback set problems on group-labelled graphs, where we aim at breaking nonnull cycles in a group-labelled graph. We obtain new FPT algorithms for these different problems. Abuilding stone for our algorithms is a general O*(4p) algorithm for a classof problems aiming at breaking a set of paths in a graph, provided thatthe set of paths has a special property called homogeneity.
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