Dominating Sets in Planar Graphs

@article{Matheson1996DominatingSI,
  title={Dominating Sets in Planar Graphs},
  author={Lesley R. Matheson and Robert E. Tarjan},
  journal={Eur. J. Comb.},
  year={1996},
  volume={17},
  pages={565-568}
}
Motivated by an application to unstructured multigrid calculations , we consider the problem of asymptotically minimizing the size of dominating sets in triangulated planar graphs . Specifically , we wish to find the smallest » such that , for n suf ficiently large , every n -vertex planar graph contains a dominating set of size at most » n . We prove that 1 – 4 < » < 1 – 3 , and we conjecture that » 5 1 – 4 . For triangulated discs we obtain a tight bound of » 5 1 – 3 . The upper bound proof… CONTINUE READING
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