On Relational Cycles

  • Alexander Fronk
  • Jörg Pleumann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)


We provide relation-algebraic characterisations of elementary, ordinary, and maximal cycles in graphs. Relational specifications for the enumeration of cycles are provided. They are executable within the RelView and RelClipse tools and appear to be useful in various applications. Particularly, cycles offer a valuable instrument for analysing Petri Nets.


Hamiltonian Cycle Maximal Cycle Elementary Cycle Relational Cycle Relational Characterisation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications. Monographs in Mathematics. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  2. 2.
    Baumgarten, B.: Petri-Netze: Grundlagen und Anwendungen. BI-Wissenschafts-Verlag (1990)Google Scholar
  3. 3.
    Behnke, R., Berghammer, R., Meyer, E., Schneider, P.: RELVIEW - A system for calculating with relations and relational programming. In: Astesiano, E. (ed.) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 318–321. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Berghammer, R., Fronk, A.: Exact computation of minimum feedback vertex sets with relational algebra. Fundamenta Informaticae 70, 1–16 (to appear, 2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Berghammer, R., Karger, B., Ulke, C.: Relational-algebraic analysis of Petri Nets with RelView. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 49–69. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  6. 6.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)CrossRefzbMATHGoogle Scholar
  7. 7.
    Esparza, J., Silva, M.: Circuits, Handles, Bridges and Nets. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483. Springer, Heidelberg (1991)Google Scholar
  8. 8.
    Fronk, A.: Using relation algebra for the analysis of Petri Nets in a CASE tool based approach. In: 2nd IEEE International Conference on Software Engineering and Formal Methods (SEFM), Beijing, pp. 396–405. IEEE, Los Alamitos (2004)Google Scholar
  9. 9.
    Fronk, A., Pleumann, J.: Relationenalgebraische Analyse von Petri-Netzen: Konzepte und Implementierung. In: Kindler, E. (ed.) Proceedings of the 11th Workshop on Algorithms and Tools for Petri Nets (AWPN), Universität Paderborn, Germany, September 2004, pp. 61–68 (2004); English version appeared in Petri Net News Letters (April 2005) Google Scholar
  10. 10.
    Fronk, A., Pleumann, J., Schönlein, R., Szymanski, O.: KURE-Java (2005),
  11. 11.
    Fronk, A., Schönlein, R.: RelClipse,
  12. 12.
    Hoffmann, T.: Fallstudien relationaler Programmentwicklung am Beispiel ausgewählter Graphdurchlaufstrategien. PhD thesis, Universität Kiel (2002)Google Scholar
  13. 13.
    Institute of Computer Science and Applied Mathematics, Faculty of Engineering, Christian-Albrechts-University of Kiel, Germany. RelView Examples - Graph- theoretic Algorithms,
  14. 14.
    Milanese, U.: KURE: Kiel University Relation Package (2003),
  15. 15.
    Schmidt, G., Ströhlein, T.: Relations and graphs. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)CrossRefzbMATHGoogle Scholar
  16. 16.
    Szymanski, O.: Relationale Algebra im dreidimensionalen Software-Entwurf – ein werkzeugbasierter Ansatz. Master’s thesis, Universität Dortmund (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexander Fronk
    • 1
  • Jörg Pleumann
    • 1
  1. 1.Software TechnologyUniversity of DortmundDortmundGermany

Personalised recommendations