New Algorithms for k-Face Cover, k-Feedback Vertex Set, and k -Disjoint Cycles on Plane and Planar Graphs

@inproceedings{Kloks2002NewAF,
  title={New Algorithms for k-Face Cover, k-Feedback Vertex Set, and k -Disjoint Cycles on Plane and Planar Graphs},
  author={Ton Kloks and Chuan-Min Lee and Jiping Liu},
  booktitle={WG},
  year={2002}
}
We present new fixed parameter algorithms for the FACE COVER problem on plane graphs. We show that if a plane graph has a face cover with at most k faces then its treewidth is bounded by O(?k). An approximate tree decomposition can be obtained in linear time, and this is used to find an algorithm computing the face cover number in time O(c?kn) for some constant c. Next we show that the problem is in linear time reducible to a problem kernel of O(k2) vertices, and this kernel can be used to… CONTINUE READING

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