PFFM and Quasi-Morishima matrices

  • Hua Wang
  • Zhao-yong You
Session 7A: Combinatorics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


In 1983, Greenberg [1] advanced an open problem “We do not have simple criterion that will enable us to characterize which elements of PFFM are quasi-Morishima and which are not.” In this paper, two algorithms of time complexity O(e) are provided.The algorithms can be used to decide which PFFM is quasi-Morishima and which is not. Here e denotes the number of edges of the researched graph. So we give an answer for the open problem.


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  1. 1.
    Greenberg, H., Richard, J., Maybee, J.:Rectangular matrices and signed graphs, SIAM. J. ALG. DISC. Meth. 4(1983)50–61Google Scholar
  2. 2.
    Gondran, M.. Graphs and algorithms. John Wiley and Sons. (1979) New YorkGoogle Scholar
  3. 3.
    Harary, F., Normar, R., Cartwright, D.:Structrual Models:An Introduction to the theory of Directed graphs. John Wiley and Sons (1965). New YorkGoogle Scholar
  4. 4.
    Harary.F.:On the notion of balance of a signed graph. Michingan Math. J. 2(1953–54)143–146Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Hua Wang
    • 1
  • Zhao-yong You
    • 1
  1. 1.Certre for Applied MathematicsXi'an Jiao-tong UniversityXi'anChina

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