Some common properties for regularizable graphs, edge-critical graphs and b-graphs

  • Claude Berge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)


  1. [1]
    B. Andrásfai, On critical graphs, Théorie des Graphes (Rome I.C.C.), Paris, (1967), 9–19.Google Scholar
  2. [2]
    C. Berge, Graphes et Hypergraphes (Dunod, Paris, 1970).Google Scholar
  3. [3]
    C. Berge, Une propriete des graphes k-stables critiques, Combinatorial Structures (Gordon and Breach, New York, 1970) 7–11.Google Scholar
  4. [4]
    C. Berge, Regularizable Graphs, Proc. I.S.I. Conference on Graph Theory, Calcutta, 1976.Google Scholar
  5. [5]
    C. Berge, Regularizable Graphs, Annals of Discrete Math. 3 (1978) 11–19.Google Scholar
  6. [6]
    R. A. Brualdi, Combinatorial Properties of symmetric non-negative matricies, Coll. Th. Combinat. Rome, 2 (1976) 99–120.Google Scholar
  7. [7]
    G. Cornuejols, W. Pulleyblank, A matching problem with side conditions, Discrete Math. 29 (1980) 135–139.Google Scholar
  8. [8]
    P. Erdös, T. Gallai, On the minimal number of vertices representing the edges of a graph, Publ. Math. Inst. Hung. Acad. Sci. 6 (1961) 181–203.Google Scholar
  9. [9]
    D. R. Fulkerson, A. J. Hoffman, M. H. McAndrew, Some properties of graphs with multiple edges, Can. J. Math. (1965) 166–177.Google Scholar
  10. [10]
    A. George, On line-critical graphs, Thesis, Vanderbilt Univ., Nashville, TN (1971).Google Scholar
  11. [11]
    A. Hajnal, A theorem on k-saturated graphs, Can. J. Math. 17 (1965) 720–772.Google Scholar
  12. [12]
    F. Jaeger, C. Payan, A class of regularizable graphs, Annals of Discrete Math. 3 (1978) 125–127.Google Scholar
  13. [13]
    M. Las Vergnas, A note on matchings, Acts Coll. Brussells, CER, 17, 1975, 255–260.Google Scholar
  14. [14]
    G. L. Nemhauser, L. E. Trotter, Vertex packings: structural properties and algorithms, Math. Programming 8 (1975) 232–248.Google Scholar
  15. [15]
    M. D. Plummer, On a family of line critical graphs, Monatsh. Math. 71 (1967) 40–48.Google Scholar
  16. [16]
    M. D. Plummer, Some covering concepts in Graphs, J. Comb. Theory B (1970) 46–48.Google Scholar
  17. [17]
    W. R. Pulleyblank, Minimum node covers and 2-bicritical graphs, Math. Programming 17 (1979) 91–103.Google Scholar
  18. [18]
    G. Ravindra, Well coverd Graphs, I.I.T. Madras (1976).Google Scholar
  19. [19]
    G. Ravindra, B-Graphs, Symposium on Graph Theory, I.S.I. (1976).Google Scholar
  20. [20]
    F. Sterboul, A characterization of the graphs in which the transversal number equals the matching number, J. Comb. Theory B 27 (1979) 228–229.Google Scholar
  21. [21]
    D. P. Sumner, Graphs with 1-factors, Proc. Am. Math. Soc. 42, 1974, 8–12.Google Scholar
  22. [22]
    L. Suranyi, On line-critical graphs, Infinite and finite sets, (North Holland, Amsterdam, 1975) 1411–1444.Google Scholar
  23. [23]
    W. Tutte, The factors of graphs, Canad. J. Math. 4 (1952) 314–328.Google Scholar
  24. [24]
    A. A. Zykov, On some properties of linear complexes, Math. USSR Sb. 24 (1949) 163–188.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Claude Berge
    • 1
  1. 1.Universite de Paris 6ParisFrance

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