Feedback Vertex Set in Mixed Graphs

A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on n vertices contains a feedback vertex set (FVS) of size at most k, in time O(47.5k ċ k! ċ n4). This is the first fixed parameter tractable algorithm for FVS that applies to both directed and undirected graphs.

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