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.
References
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.
M.A. Buckinghan, ‘Circle graphs', Ph.D. Dissertation, Report no. NSO-21, Courant Institute of Mathematical Sciences, 1980.
Hossam A. ElGindy, ‘Hierarchical decomposition of polygons with applications', Ph.D. Dissertation, McGill University, April 1985.
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.
M.C. Golumbic, ‘Algorithmic graph theory and perfect graphs', Academic Press, 1980.
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.
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.
J. O'Rourke, Art gallery theorems and algorithms, Oxford University Press, 1987.
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.
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.
Author information
Authors and Affiliations
Editor information
Rights 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