Outerplanar crossing numbers, the circular arrangement problem and isoperimetric functions

Electronic Journal of Combinatorics

Volumn 11, Issue 1 R, 2004, Pages 1-20

  Czabarka, Éva ^a   Székely, László A ^b   Sýkora, Ondrej ^c   Vrt'o, Imrich ^d  

^a The College of William and Mary   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

^c LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^d INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 8844285278     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1834     Document Type: Article

References (22)

1. Bezrukov, S., Schroeder, U.-P., The cyclic wirelength of trees, Discrete Appl. Math. 87 (1998), 275-277.
2. Bollobás, B., Leader, I., Edge-isoperimetric inequalities in the grid, Combinatorica, 11 (1991), 299-314.
3. Ching-Jung Guu, The circular wirelength problem for the hypercube, Ph.D. Thesis, University of California, Riverside, 1997.
4. Chung, F.R.K., Füredi, Z., Graham, R.L., Seymour, P.D.: On induced subgraphs of the cube, J. Comb. Theory A-49 (1988), 180-187.
5. Crimmins, R., T., Horwitz, H.M., Palermo, C. J., Minimization of mean-square error for data transmitted via group codes, IEEE Trans. Information Theory 15 (1969) 72-78.
6. Di Battista, J., Eades, P., Tamassia, R., Tollis, I. G., Graph Drawing. Algorithms for the Visualization of Graphs, Prentice Hall Inc., Upper Saddle River, NJ, 1999, 432 pp.
7. Gauyacq, G., Forwarding index of cayley graphs and star graphs, Discrete Applied Mathematics 80 (1997), 149-160.
8. Heydemann, M.C., Meyer, J.C., Sotteau, D., On forwarding indices of networks, Discrete Applied Mathematics 23 (1989), 103-123.
9. Juvan, M., Mohar, B., Optimal linear labelings and eigenvalues of graphs, Discrete Appl. Math. 36 (1992) 153-168.
10. Kainen, P.C., The book thickness of a graph II, Congressus Numerantium, 71 (1990), 121-132.
11. Pach, J., Shahrokhi F., and Szegedy, M., Applications of crossing numbers, in: Proc. 10-th Annual ACM Symposium on Computational Geometry (ACM, New York, 1994); and Algorithmica 16 (1996) 111-117.
12. Pach, J., Shahrokhi F., and Szegedy, M., Applications of crossing numbers, in: Proc. 10-th Annual ACM Symposium on Computational Geometry (ACM, New York, 1994); and Algorithmica 16 (1996) 111-117.
13. Purchase, H., Which aesthetic has the greatest effect on human understanding?, in: Proc. Symposium on Graph Drawing, GD'97, Lecture Notes in Computer Science 1353 Springer, 1997, 248-261.
14. Shahrokhi, F., Sýkora, O., Székely, L. A., and Vrťo, I., Crossing numbers: bounds and applications, in: Intuitive Geometry, eds. I. Bárány and K. Böröczky, Bolyai Society Mathematical Studies 6, János Bolyai Mathematical Society, Budapest, 1997, 179-206.
15. Shahrokhi, F., Sýkora, O., Székely, L.A., Vrt'o, I., Book embeddings and crossing numbers, in: Proc. 20th Intl. Workshop on Graph-Theoretic Concepts in Computer Science, WG'94, Lecture Notes in Computer Science 903, Springer, 1995, 256-268.
16. Shahrokhi, F., Sýkora, O., Székely, L.A., Vrt'o, I., Towards the theory of convex crossing numbers, In: Towards a Theory of Geometric Graphs, ed. J. Pach, Contemporary Mathematics, 342 American Mathematical Society, Providence 2004, 249-258.
17. Shahrokhi, F., Székely, L.A., An algebraic approach to the uniform concurrent multi-commodity flow problem: Theory and applications, Technical Report CRPDC-91-4, DCS, Uni. North Texas, Denton, 1991.
18. Shahrokhi., F., Székely, L. A., Constructing integral uniform flows in symmetric networks and application to the forwarding index problem, Discrete Applied Math. 108 (2001), 175-191.
19. Sýkora, O., Vrt'o, I., On the crossing number of hypercubes and cube conected cycles, BIT 33 (1993), 232-237.
20. Székely, L. A., Crossing numbers and hard Erdos problems in discrete geometry, Combinatorics, Probability, and Computing 6(3)(1997), 353-358.
21. Székely, L.A., A successful concept for measuring non-planarity of graphs: the crossing number, Discrete Math. 276 (2003), 1-3, 331-352.
22. Tillich, J.-P., Edge isoperimetric inequalities for product graphs, Discrete Mathematics 213 (2000), 291-320.