Skip to main content

On recognizing and characterizing visibility graphs of simple polygons

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 318))

Abstract

In this paper, we establish three necessary conditions for recognizing visibility graphs of simple polygons and conjecture that these conditions are sufficient. We also show that visibility graphs of simple polygons do not posses the characteristics of several special classes of graphs.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Avis and D. Rappaport, ‘Computing the largest empty convex subset of a set of points', Proceedings of the first ACM symposium on computational geometry, pp. 161–167, 1985.

    Google Scholar 

  2. M.A. Buckinghan, ‘Circle graphs', Ph.D. Dissertation, Report no. NSO-21, Courant Institute of Mathematical Sciences, 1980.

    Google Scholar 

  3. Hossam A. ElGindy, ‘Hierarchical decomposition of polygons with applications', Ph.D. Dissertation, McGill University, April 1985.

    Google Scholar 

  4. F. Gavril, ‘Algorithms for minimum colouring, maximum clique, minimum convering by cliques, and maximum independent set of a chordal graph', SIAM Journal on Computing, vol. 1, no.2, pp. 180–187, 1972.

    Google Scholar 

  5. M.C. Golumbic, ‘Algorithmic graph theory and perfect graphs', Academic Press, 1980.

    Google Scholar 

  6. C.P. Gabor, W. Hsu and K.J. Supowit, ‘Recognizing circle graphs in polynomial time', Proceedings of 26th IEEE Annual Symposium on Foundation of Computer Science, pp.106–116, 1985.

    Google Scholar 

  7. T. Lazano-Perez and M.A. Wesley, ‘An algorithm for planning collision-free paths among polygonal obstacles', Commun. of ACM, vol. 22, pp.560–570, 1979.

    Google Scholar 

  8. J. O'Rourke, Art gallery theorems and algorithms, Oxford University Press, 1987.

    Google Scholar 

  9. A. Pnueli, A. Lempel and S. Even, ‘Transitive orientation of graphs and identification of permutation graphs', Canadian Journal of Mathematics, vol.23, no.1, pp. 160–175, 1971.

    Google Scholar 

  10. L.G. Shapiro and R.M. Haralick, ‘Decomposition of two-dimentional shape by graph-theoretic clustering', IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-1, no.1, pp. 10–19, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Rolf Karlsson Andrzej Lingas

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ghosh, S.K. (1988). On recognizing and characterizing visibility graphs of simple polygons. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-19487-8_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19487-3

  • Online ISBN: 978-3-540-39288-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics