A characterization of planar graphs by pseudo-line arrangements

Algorithmica (New York)

Volumn 35, Issue 3, 2003, Pages 269-285

  Tamaki, Hisao ^a   Tokuyama, Takeshi ^b  

^a MEIJI UNIVERSITY   (Japan)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Geometric graph theory; k Level complexity; Planar graph; Pseudo line arrangement

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; CONFORMAL MAPPING; CURVE FITTING; EQUIVALENCE CLASSES; OPTIMIZATION; THEOREM PROVING;

GEOMETRIC GRAPH THEORY; PARAMETRIC MATROID OPTIMIZATION; PLANAR GRAPHS; PSEUDO-LINE ARRANGEMENTS; PSEUDO-LINE GRAPHS;

GRAPH THEORY;

EID: 0942279286     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-002-0999-9     Document Type: Article

References (16)

1. P.K. Agarwal, B. Aronov, and M. Sharir, On Levels in Arrangements of Lines, Segments, Planes, and Triangles, Proc. 13th Symposium on Computational Geometry, 1997, pp. 30-38.
2. M. Ajtai, V. Chvátal, M.M. Newborn, and E. Szemerédi, Crossing-Free Subgraphs, Ann. Discrete Math., 12 (1982), 9-12.
3. T.K. Dey, Improved Bounds on Planar k-Sets and k-Levels, Proc. 38th FOCS, 1997, pp. 156-161.
4. H. Edelsbrunner, Algorithms in Combinatorial Geometry, EATCS Monographs on TCS 10, 1987, Springer-Verlag, New York.
5. D. Eppstein, Geometric Lower Bounds for Parametric Matroid Optimization, Proc. 27th ACM Symposium on Theory of Computing, 1995, pp. 662-671.
6. P. Erdös, L. Lovaśz, A. Simmons, and E.G. Straus, Dissection Graphs of Planar Point Sets, in A Survey of Combinatorial Theory, J.N. Srivastava et al., eds., pp. 139-149, 1973, North-Holland, Amsterdam.
7. I. Fáry, On Straight Line Representation of Planar Graphs. Acta Sci. Math. Szeged., 11 (1948), 229-233.
8. 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., pp. 103-134, 1993, Springer-Verlag, New York.
9. D. Gusfield, Bounds for the Parametric Spanning Tree Problem, Proc. Humbolt Conference on Graph Theory, Combinatorics, and Computing, 1979, pp. 173-183.
10. 1+ω(1+√log n) Transpositions at the Median, Unpublished manuscript, 1982.
11. L. Lovász, On the Number of Halving Lines, Ann. Univ. Sci. Budapest Eötvös, Sect. Math., 14 (1971), 107-108.
12. J. Matoušek, Combinatorial and Algorithmic Geometry, Unpublished lecture notes, 1996.
13. G.H. Meister, Polygons Have Ears, Amer. Math. Monthly, 82 (1975), 648-651.
14. J. Pach and P.K. Agarwal, Combinatorial Geometry, Wiley, 1995.
15. J. Pach, W. Steiger, and E. Szemerédi, An Upper Bound on the Number of Planar K-Sets, Discrete Comput. Geom., 7 (1992), 109-123.
16. H. Tamaki and T. Tokuyama, How to Cut Psuedo-Parabolas into Segments, Discrete Comput. Geom., 19 (1998), 265-290.