Representations by contact and intersection of segments

Algorithmica (New York)

Volumn 47, Issue 4, 2007, Pages 453-463

  De Fraysseix, Hubert ^a   De Mendez, Patrice Ossona ^a  

^a ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES   (France)

Author keywords

Contact representation; Contacts of segments; Graph representation; Intersection of segments; Intersection representation

Indexed keywords

BIPARTITE GRAPHS; CONTACT REPRESENTATION; GRAPH REPRESENTATION; INTERSECTION REPRESENTATION;

CARBON; COLOR;

GRAPH THEORY;

EID: 33947584273     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-006-0157-x     Document Type: Conference Paper

References (30)

1. J. Czyziwicz, E. Kranakis, and J. Urrutia, A simple proof of the representation of bipartite planar graphs as the contact graphs of orthogonal straight line segments, Information Processing Letters 66(3) (1998), 125-126.
2. N. de Castro, F. J. Cobos, J.C. Dana, and A. Marquez, Triangle-free planar graphs as segment intersection graphs, Journal of Graph Algorithms and Applications 6(1) (2002), 7-26.
3. G. Ehrlich, S. Even, and R.E. Tarjan, Intersection graphs of curves in the plane, Journal of Combinatorial Theory, Series B 21 (1986), 8-20.
4. H. de Fraysseix, Local complementation and interlacement graphs, Discrete Mathematics 33 (1981), 29-35.
5. H. de Fraysseix, A characterization of circle graphs, European Journal of Combinatorics 5 (1984), 223-238.
6. H. de Fraysseix and P. Ossona de Mendez, Intersection Graphs of Jordan Arcs, Contemporary Trends in Discrete Mathematics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 49, DIMATIA-DIMACS, 1999, Štirin 1997 Proc., pp. 11-28.
7. H. de Fraysseix and P. Ossona de Mendez, On a characterization of Gauss codes, Discrete and Computational Geometry 22(2) (1999), 287-295.
8. H. de Fraysseix and P. Ossona de Mendez, Stretching of Jordan arc contact systems, in Graph Drawing, Lecture Notes in Computer Science, vol. 2912, Springer-Verlag, Berlin, 2004, pp. 71-85.
9. H. de Fraysseix and P. Ossona de Mendez, Stretching of jordan arc contact systems, Discrete Applied Mathematics (2006), in press.
10. H. de Fraysseix, P. Ossona de Mendez, and J. Pach, Representation of planar graphs by segments, Intuitive Geometry 63 (1991), 109-117.
11. H. de Fraysseix, P. Ossona de Mendez, and P. Rosenstiehl, On triangle contact graphs, Combinatorics, Probability and Computing 3 (1994), 233-246.
12. C.F. Gauss, Werke, Teubner, Leipzig, 1900, pp. 272 and 282-285.
13. J.E. Goodman and R. Pollack, Allowable sequences and order types in discrete and computational geometry, in New Trends in Discrete and Computational Geometry (J. Pach, ed.), Springer-Verlag, New York, 1993, pp. 103-134.
14. B. Grünbaum, Arrangements and Spreads, American Mathematical Society, Providence, RI, 1972.
15. I.B.-A. Hartman, I. Newman, and R. Ziv, On grid intersection graphs, Discrete Mathematics 87 (1991), 41-52.
16. PetrHliněny, Contact graphs of line segments are NP-complete, Discrete Mathematics 235(1-3) (2001), 95-106.
17. J. Kratochvíl, String graphs I: the number of critical nonstring graphs is infinite, Journal of Combinatorial Theory, Series B 52 (1991), 53-66.
18. J. Kratochvíl, String graphs II: Recognizing string graphs is NP-hard, Journal of Combinatorial Theory, Series B 52 (1991), 67-78.
19. J. Kratochvíl and J. Matoušek, String graphs requiring exponential representations, Journal of Combinatorial Theory, Series B 52 (1991), 1-4.
20. J. Kratochvíl and J. Matoušek, Intersection graphs of segments, Journal of Combinatorial Theory, Series B 62(2) (1994), 289-315.
21. F. Levi, Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade, Ber. Math.-Phys. Kl. sächs. Akad. Wiss. 78 (1926), 251-267.
22. N.E. Mnëv, On manifolds of combinatorial types of projective configurations and convex polyhedra, Soviet Mathematics Doklady 32 (1985), 335-337.
23. N.E. Mnëv, The universality theorems on the classification problem of configuration varieties and convex polytopes varieties, in Topology and Geometry - Rohlin Seminar (Berlin) (O. Ya. Viro, ed.), Lecture Notes in Mathematics, vol. 1346, Springer-Verlag, New York, 1988, pp. 527-544.
24. J. Fach and G. Tóth, Which crossing number is it anyway?, Journal of Combinatorial Theory, Series B 80(2) (2000), 225-246.
25. J. Richter-Gebert, Realization Spaces of Polytopes, Lecture Notes in Mathematics, vol. 1643, Springer-Verlag, New York, 1996.
26. P. Rosenstiehl, A new proof of the Gauss interlace conjecture, Advances in Applied Mathematics 23(1) (1999), 3-13.
27. M. Schaefer, E. Sedgwick, and D. Štefankovič, Recognizing string graphs in NP, Journal of Computer and System Sciences 67(2) (2003), 365-380.
28. E.R. Scheinerman, Intersection classes and multiple intersection parameters of graphs, Ph.D. thesis, Princeton University, 1984.
29. P. W. Shor, Stretchability of Pseudolines is NP-Hard, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 4, American Mathematical Society, Providence, RI, 1991, pp. 531-554.
30. F.W. Sinden, Topology of thin RC-circuits, Bell System Technical Journal (1966), 1639-1662.