Drawings of planar graphs with few slopes and segments

Computational Geometry: Theory and Applications

Volumn 38, Issue 3, 2007, Pages 194-212

  Dujmović, Vida ^a   Eppstein, David ^b   Suderman, Matthew ^c   Wood, David R ^d  

^a MCGILL UNIVERSITY   (Canada)

^b Irvine   (United States)

^c MCGILL UNIVERSITY   (Canada)

^d UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Canonical decomposition; Graph drawing; Planar graph; Segment; Slope

Indexed keywords

EID: 84867948399     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2006.09.002     Document Type: Article

References (26)

1. J. Barát, J. Matoušek, and D.R. Wood Bounded-degree graphs have arbitrarily large geometric thickness Electron. J. Combin. 13 1 2006 R3
2. J. Bhasker, and S. Sahni A linear time algorithm to check for the existence of a rectangular dual of a planar triangulated graph Networks 17 3 1987 307 317
3. J. Bhasker, and S. Sahni A linear algorithm to find a rectangular dual of a planar triangulated graph Algorithmica 3 2 1988 247 278
4. J. Czyzowicz, E. Kranakis, and J. Urrutia A simple proof of the representation of bipartite planar graphs as the contact graphs of orthogonal straight line segments Inform. Process. Lett. 66 3 1998 125 126
5. N. de Castro, F.J. Cobos, J.C. Dana, A. Márquez, and M. Noy Triangle-free planar graphs as segment intersection graphs J. Graph Algorithms Appl. 6 1 2002 7 26
6. H. de Fraysseix, and P. Ossona de Mendez Contact and intersection representations J. Pach, Proc. 12th International Symp. on Graph Drawing (GD '04) Lecture Notes in Comput. Sci. vol. 3383 2004 Springer Berlin 217 227
7. H. de Fraysseix, P. Ossona de Mendez, and J. Pach A left-first search algorithm for planar graphs Discrete Comput. Geom. 13 3-4 1995 459 468
8. H. de Fraysseix, J. Pach, and R. Pollack How to draw a planar graph on a grid Combinatorica 10 1 1990 41 51
9. G.A. Dirac On rigid circuit graphs Abh. Math. Sem. Univ. Hamburg 25 1961 71 76
10. V. Dujmović, M. Suderman, and D.R. Wood Graph drawings with few slopes Comput. Geom. 38 3 2007 181 193 this issue
11. V. Dujmović, and D.R. Wood Graph treewidth and geometric thickness parameters P. Healy, N.S. Nikolov, Proc. 13th International Symp. on Graph Drawing (GD '05) Lecture Notes in Comput. Sci. vol. 3843 2006 Springer Berlin 129 140 http://arxiv.org/math/0503553
12. I. Fáry On straight line representation of planar graphs Acta Univ. Szeged. Sect. Sci. Math. 11 1948 229 233
13. A. Garg, and R. Tamassia On the computational complexity of upward and rectilinear planarity testing SIAM J. Comput. 31 2 2001 601 625
14. I. Ben-Arroyo Hartman, I. Newman, and R. Ziv On grid intersection graphs Discrete Math. 87 1 1991 41 52
15. G. Kant Hexagonal grid drawings E.W. Mayr, Proc. 18th International Workshop in Graph-Theoretic Concepts in Computer Science (WG '92) Lecture Notes in Comput. Sci. vol. 657 1993 Springer Berlin 263 276 Also see Tech. Rep. RUU-CS-92-06, Universiteit Utrecht, Netherlands, 1992
16. G. Kant Drawing planar graphs using the canonical ordering Algorithmica 16 1 1996 4 32
17. P. Ossona de Mendez, and H. de Fraysseix Intersection graphs of Jordan arcs Contemporary Trends in Discrete Mathematics DIMACS Ser. Discrete Math. Theoret. Comput. Sci. vol. 49 1999 Amer. Math. Soc. Providence, RI 11 28
18. J. Pach, and D. Pálvölgyi Bounded-degree graphs can have arbitrarily large slope numbers Electron. J. Combin. 13 1 2006 N1
19. Md.S. Rahman, S.-I. Nakano, and T. Nishizeki Rectangular grid drawings of plane graphs Comput. Geom. 10 3 1998 203 220
20. Md.S. Rahman, S.-I. Nakano, and T. Nishizeki A linear algorithm for bend-optimal orthogonal drawings of triconnected cubic plane graphs J. Graph Algorithms Appl. 3 1999 31 62
21. Md.S. Rahman, S.-I. Nakano, and T. Nishizeki Box-rectangular drawings of plane graphs J. Algorithms 37 2 2000 363 398
22. Md.S. Rahman, S.-I. Nakano, and T. Nishizeki Rectangular drawings of plane graphs without designated corners Comput. Geom. 21 3 2002 121 138
23. Md.S. Rahman, T. Nishizeki, and S. Ghosh Rectangular drawings of planar graphs J. Algorithms 50 2004 62 78
24. C. Thomassen Plane representations of graphs Progress in Graph Theory 1984 Academic Press Toronto 43 69
25. P. Ungar On diagrams representing maps J. London Math. Soc. 28 1953 336 342
26. K. Wagner Bemerkung zum Vierfarbenproblem Jber. Deutsch. Math.-Verein. 46 1936 26 32