, Volume 6, Issue 1, pp 23–27 | Cite as

A parity digraph has a kernel

  • Mostafa Blidia


We show that every digraph has a kernel (i.e. an absorbing and independent set) under the following parity condition: For every pair of verticesx, y x ≠ y all minimal directed paths betweenx andy have the same length parity.

AMS subject classification (1980)

05 C 20 


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  1. [1]
    C. Berge,Graphes et Hypergraphes, Dunot 1970.Google Scholar
  2. [2]
    M. Blidia, Kernels in parity graphs with an orientation condition, to appear.Google Scholar
  3. [3]
    P. Duchet, Graphes noyaux parfaits,Ann. Disc. Math. 9 (1980) 93–102.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    H. Galeana-Sanchez, A theorem about a conjecture of H. Meyniel on kernel perfect graph,Universidad Nacional A de Mexico.Google Scholar
  5. [5]
    H. Meyniel, Contribution à l’étude de quelques problèmes en théorie des graphes (Circuits hamiltoniens, coloration, noyaux),Thèse Paris VI (1982).Google Scholar
  6. [6]
    V. Neumann-Lara, Seminucleos de une digrafica,Annales del Instituto de Matematicas 11 (1971),Universidad Nacional A de Mexico.Google Scholar
  7. [7]
    J. Von Neumann andO. Morgenstern,Theory of games and economic behavior, Princeton University Press, Princeton 1944.zbMATHGoogle Scholar
  8. [8]
    M. Richardson, Solutions of irreflexive relations,Annals of Math. 58 (1953), 573–580.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • Mostafa Blidia
    • 1
  1. 1.U.E.R. 48 Mathématiques (E.R.175)Université Pierre et Marie CurieParis

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