Fractional Lengths and Crossing Numbers

  • Ondrej Sýkora
  • László A. Székely
  • Imrich Vrt’o
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)


Adamec and Nešetřil [1] proposed a new the so called fractional length criterion for measuring the aesthetics of (artistic) drawings. They proposed to apply the criterion to the aesthetic drawing of graphs. In the graph drawing community, it is widely believed and even experimentally confirmed that the number of crossings is one of the most important aesthetic measures for nice drawings of graphs [6]. The aim of this note is to demonstrate on two standard graph drawing models that in provably good drawings, with respect to the crossing number measure, the fractional length criterion is closely related to the crossing number criterion.


  1. 1.
    Adamec, J., Nešetřil, J.: Towards an Aesthetic Invariant for Graph Drawing. In: 9th Intl. Symp. on Graph Drawing. LNCS 2265. Springer. Berlin (2001) 287–296Google Scholar
  2. 2.
    Bhatt, S., Leighton, F. T.: A Framework for Solving VLSI Graph Layout Problems. J. Computer and System Science 28 (1984) 300–334Google Scholar
  3. 3.
    Di Battista, G., Eades, P., Tollis, I., Tamassia, R.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall (1999)Google Scholar
  4. 4.
    Leighton, F. T.: New Lower Bound Techniques for VLSI. MathematicalSystems Theory 17 (1984) 47–70MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Leiserson, C. E.: Area Efficient Graph Layouts (for VLSI). In: 21st AnnualSymp osium on Foundations of Computer Science. IEEE Press (1980) 270–281Google Scholar
  6. 6.
    Purchase, H.: Which aestethic has the greatest effect on Human Understanding? In: 5th Intl. Symp. on Draph Drawing. LNCS 1353. Springer. Berlin (1997) 248–261Google Scholar
  7. 7.
    Shahrokhi, F., Sýkora, O., Székely, L. A., Vrt’o, I.: On Bipartite Drawings and the Linear Arrangement Problem. SIAM J. Computing 30 (2000), 1773–1789.CrossRefGoogle Scholar
  8. 8.
    Steinhaus, H.: Length, Shape and Area. Colloquium Math. III (1954) 1–13MathSciNetGoogle Scholar
  9. 9.
    Thompson, C. D.: Area-Time Complexity for VLSI. In: 11th Annual ACM Symposium on Theory of Computing. ACM Press (1979) 81–89Google Scholar
  10. 10.
    Valiant, L. G.: Universality Considerations in VLSI Circuits. IEEE Transactions on Computers 30 (1981) 135–140MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ondrej Sýkora
    • 1
  • László A. Székely
    • 2
  • Imrich Vrt’o
    • 3
  1. 1.Department of Computer ScienceLoughborough University LoughboroughLeicestershireUK
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  3. 3.Institute of MathematicsSlovak Academy of SciencesBratislavaSlovak Republic

Personalised recommendations