Feedback vertex set in mixed graphs

Authors:
Paul Bonsma;Daniel Lokshtanov
Affiliations:
Humboldt-Universität zu Berlin, Institut für Informatik, Berlin, Germany;University of California, San Diego, Department of Computer Science and Engineering, La Jolla, CA
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

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.