Stretching of Jordan Arc Contact Systems

De Fraysseix, Hubert and Ossona de Mendez, Patrice (2004) Stretching of Jordan Arc Contact Systems. In: Graph Drawing 11th International Symposium, GD 2003, September 21-24, 2003, Perugia, Italy , pp. 71-85 (Official URL: http://dx.doi.org/10.1007/978-3-540-24595-7_7).

Full text not available from this repository.

Abstract

We prove that a contact system of Jordan arcs is stretchable if and only if it is extendable into a weak arrangement of pseudo-lines.

Item Type:Conference Paper
Additional Information:10.1007/978-3-540-24595-7_7
Classifications:Z Theory > Z.250 Geometry
ID Code:428

Repository Staff Only: item control page

References

E. Colin de Verdière, M. Pocchiola, and G. Vegter, Tutte's barycenter method applied to isotopies, Proc. 13th Canad. Conf. Comput. Geom., 2001.

I. Fáry, On straight lines representation of planar graphs, Acta Scientiarum Mathematicarum (Szeged) II (1948), 229-233.

M. Linial, L. Lovász, and A. Wigdersib, Rubber bands, convex embeddings and graph connectivity, Combinatorica 8 (1988), no. 1, 91-102.

D. Orden, Two problems in geometric combinatorics: Efficient triangulations of the hypercube; plane graphs and rigidity., Ph.D. thesis, University of Santander, Spain, 2003.

P. W. Shor, Stretchability of pseudolines is NP-hard, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 4 (1991), 531-554.

S. K. Stein, Convex maps, Proc. Amer. Math. Soc., vol. 2, 1951, pp. 464-466.

E. Steinitz and H. Rademacher, Vorlesung über die Theorie der Polyeder, Springer, Berlin, 1934.

C. Thomassen, Planarity and duality of finite and infinite planar graphs, J. Combinatorial Theory, Series B 29 (1980), 244-271.

W. T. Tutte, Convex representations of graphs, Proc. London Math. Society, vol. 10, 1960, pp. 304-320.

W. T. Tutte, How to draw a graph, Proc. London Math. Society, vol. 13, 1963, pp. 743-768.

K. Wagner, Über die Eigenschaft der Ebenen Komplexe, Math. Ann. 114 (1937), 570-590.