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Connected proper interval graphs and the guard problem in spiral polygons

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  • Graph Theory
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1120))

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References

  1. A. A. Bertossi, The edge Hamiltonian path problem is NP-complete, Inform. Process. Lett. 13 (1982) 157–159.

    Article  Google Scholar 

  2. A. A. Bertossi, Finding Hamiltonian circuits in proper interval graphs, Inform. Process. Lett. 17 (1983) 97–101.

    Article  Google Scholar 

  3. G. Ding, Convering the edges with consecutive sets, J. Graph Theory 15 (1991) 559–562.

    Google Scholar 

  4. H. Evertt and D. G. Corneil, Recognizing visibility graphs of spiral polygons, J. Algorithms 11 (1990) 1–26.

    Article  Google Scholar 

  5. D. R. Fulkerson and O. A. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965) 835–855.

    Google Scholar 

  6. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco (1979).

    Google Scholar 

  7. M. R. Garey, D. S. Johnson, and R. E. Tarjan, The planar Hamiltonian circuit problem is NP-complete, SIAM J. Comput. 5 (1976) 704–714.

    Article  Google Scholar 

  8. F. Gavril, Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of a chordal graph, SIAM J. Comput. 1 (1972) 180–187.

    Article  Google Scholar 

  9. P. C. Gilmore and A. J. Hoffman, A characterization of comparability graphs and of interval graphs, Canad. J. Math. 16 (1964) 539–548.

    Google Scholar 

  10. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York (1980).

    Google Scholar 

  11. D. Gouyou-Beauchamps, The Hamiltonian circuit problem is polynomial for 4-connected planar graphs, SIAM J. Comput. 11 (1982) 529–539.

    Article  Google Scholar 

  12. A. Itai, C. H. Papadimitriou, and J. L. Szwarcfiter, Hamiltonian paths in grid graphs, SIAM J. Comput. 11 (1982) 676–686.

    Article  Google Scholar 

  13. R. M. Karp, Reducibility among combinatorial problems, in: Complexity of Computer Computation (eds. R. E. Miller and J. W. Thatcher) Plenum Press, New York (1972) 85–103.

    Google Scholar 

  14. J. M. Keil, Finding Hamiltonian circuits in interval graphs, Inform. Process. Lett. 20 (1985) 201–206.

    Article  Google Scholar 

  15. M. S. Krishnamoorthy, An NP-hard problem in bipartite graphs, SIGACT News 7 (1975) 26.

    Article  Google Scholar 

  16. G. K. Manacher, T. A. Mankus, and C. J. Smith, An optimum Θ(nlogn) algorithm for finding a canonical Hamiltonian path and a canonical Hamiltonian circuit in a set of intervals, Inform. Process. Lett. 35 (1990) 205–211.

    MathSciNet  Google Scholar 

  17. J. O'Rourke, Art Gallery Theorems and Algorithms, Oxford University Press, New York (1987).

    Google Scholar 

  18. F. S. Roberts, Representations of Indifference Relations, Ph.D. thesis, Stanford University (1968).

    Google Scholar 

  19. F. S. Roberts, Indifference graphs, in: Proof Techniques in Graph Theory (ed. F. Harary) Academic Press, New York (1969) 139–146.

    Google Scholar 

  20. W. K. Shih, T. C. Chern, and W. L. Hsu, An O(n 2logn) algorithm for the Hamiltonian cycle problem on circular-arc graphs, SIAM J. Comput. 21 (1992) 1026–1046.

    Article  Google Scholar 

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Michel Deza Reinhardt Euler Ioannis Manoussakis

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© 1996 Springer-Verlag Berlin Heidelberg

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Chen, C., Chang, CC. (1996). Connected proper interval graphs and the guard problem in spiral polygons. In: Deza, M., Euler, R., Manoussakis, I. (eds) Combinatorics and Computer Science. CCS 1995. Lecture Notes in Computer Science, vol 1120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61576-8_71

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  • DOI: https://doi.org/10.1007/3-540-61576-8_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61576-7

  • Online ISBN: 978-3-540-70627-4

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