Splitting (complicated) surfaces is hard. Chambers, E. W., Colin de Verdière, É., Erickson, J., Lazarus, F., & Whittlesey, K. In Proceedings of Symposium on Computational Geometry (SoCG), pages 421-429, 2006.
Splitting (complicated) surfaces is hard [link]Paper  bibtex   
@inproceedings{ dblp2767542,
  title = {Splitting (complicated) surfaces is hard},
  author = {Erin W. Chambers and Éric Colin de Verdière and Jeff Erickson and Francis Lazarus and Kim Whittlesey},
  author_short = {Chambers, E. W. and Colin de Verdière, É. and Erickson, J. and Lazarus, F. and Whittlesey, K.},
  bibtype = {inproceedings},
  type = {inproceedings},
  year = {2006},
  key = {dblp2767542},
  id = {dblp2767542},
  biburl = {http://www.dblp.org/rec/bibtex/conf/compgeom/ChambersVELW06},
  url = {http://doi.acm.org/10.1145/1137856.1137918},
  conference = {SoCG},
  pages = {421-429},
  text = {SoCG 2006:421-429},
  booktitle = {Proceedings of Symposium on Computational Geometry (SoCG)}

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