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Le théorème du coloriage des cartes [ex-conjecture de Heawood et conjecture des quatre couleurs]

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Séminaire Bourbaki vol. 1977/78 Exposés 507–524

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 710))

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Bibliographie

  1. A. B. KEMPE-On the geographical problem of the four colours, Amer. J. Math., 2(1879), 193–200.

    Article  MathSciNet  Google Scholar 

  2. P. J. HEAWOOD-Map colour theorem, Quart. J. Math., 24(1890), 332–338.

    MATH  Google Scholar 

  3. G. D. BIRKHOFF-The reducibility of maps, Amer. J. Math., 35(1913), 114–128.

    Article  MathSciNet  Google Scholar 

  4. H. LEBESGUE-Quelques conséquences simples de la formule d’Euler, J. de Math., 9, Sér. 19 (1940), 27–43.

    MATH  MathSciNet  Google Scholar 

  5. G. A. DIRAC-Map-colour theorems, Can. J. Math., 4(1952), 480–490. Repris dans Short proof of a map-colour theorem, Can. J. Math., 9(1957), 225–226.

    MATH  MathSciNet  Google Scholar 

  6. G. A. DIRAC-Map-colour theorems related to the Heawood colour formula, J. Lond. Math. Soc., 31(1956), 460–471 et 32(1957), 436–455.

    MATH  MathSciNet  Google Scholar 

  7. H. HADWIGER-Ungelöste Probleme, Element. Math., 13(1958), 127–128.

    Google Scholar 

  8. K. WAGNER-Bemerkungen zur Hadwigers Vermutung, Math. Annalen, 141(1960), 433–451.

    Article  MATH  Google Scholar 

  9. J. W. T. YOUNGS-Minimal imbeddings and the genus of a graph, J. Math. Mech., 12(1963), 303–314.

    MATH  MathSciNet  Google Scholar 

  10. W. GUSTIN-Orientable embedding of Cayley graphs, Bull. Amer. Math. Soc., 69 (1963), 272–275.

    Article  MATH  MathSciNet  Google Scholar 

  11. O. ORE-The four-color problem, Pure and Applied Maths., 27, Acad. Press New York-London, 1967.

    Google Scholar 

  12. J. W. T. YOUNGS-The Heawood map-colouring conjecture, Chapter 12 in Graph Theory and Theoretical physics (F. Harary ed.), Acad. Press New York-London, 1967, 313–354.

    Google Scholar 

  13. W. MADER-Homorphiesätze für Graphen, Math. Annalen, 178(1968), 154–168.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. HEESCH-Untersuchungen zum Vierfarbenproblem, B.I. Hochschulskripten 810/810a/810b, Bibliographische Institute Mannheim-Vienna-Zürich, 1969.

    Google Scholar 

  15. N. BIGGS-Classification of complete maps on orientable surfaces, Rend. Matematica (VI), 4(1971), 645–655.

    MathSciNet  Google Scholar 

  16. H. MAHNKE-The necessity of non-abelian groups in the case 0 of the Heawood map-coloring theorem, J. Comb.Theory, 13(1972), 263–265.

    Article  MATH  MathSciNet  Google Scholar 

  17. W. TUTTE-H. WHITNEY-Kempe chains and the four color problem, Utilitas Mathemetica, 2(1972), 241–281.

    MATH  MathSciNet  Google Scholar 

  18. G. RINGEL-Map color theorem, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Band 209, Springer-Verlag, Berlin-New York, 1974, 191 pages.

    MATH  Google Scholar 

  19. M. JUNGERMAN-Orientable triangular embeddings of K18 − K3 and K13 − K3, J. Comb. Theory (B), 16(1974), 293–294.

    MATH  MathSciNet  Google Scholar 

  20. J. L. GROSS-Voltage graphs, Discrete Mathematics, 9(1974), 239–246.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. L. GROSS-T. W. TUCKER-Quotients of complete graphs: revisiting the Heawood map-colouring problem, Pacific J. Math., 55(1974), 391–402.

    MATH  MathSciNet  Google Scholar 

  22. M. JUNGERMAN-The genus of Kn − K2, J. Comb. Theory (B), 18(1975), 53–58.

    MATH  MathSciNet  Google Scholar 

  23. M. JUNGERMAN-A new solution for the non-orientable case 1 of the Heawood map color theorem, J. Comb. Theory (B), 19(1975), 69–71.

    MATH  MathSciNet  Google Scholar 

  24. S. R. ALPERT-J. L. GROSS-Components of branohed coverings of current graphs, J. Comb. Theory (B), 20(1976), 283–303.

    MATH  MathSciNet  Google Scholar 

  25. G. RINGEL-The combinatorial map color theorem, J. Graph Theory 1 (Summer 1977), 141–155.

    MATH  MathSciNet  Google Scholar 

à paraître

  1. K. APPEL-W. HAKEN-Every planar map is four colorable, Part I: discharging, Part II: reducibility, Illinois J. Math.

    Google Scholar 

  2. K. APPEL-W. HAKEN-J. MAYER-Triangulations à V5 séparés dans le problème des quatre couleurs.

    Google Scholar 

  3. R. RINGEL-Non-existence of graph embeddings, Theory and Applications of graphs, Springer-Verlag.

    Google Scholar 

  4. M. JUNGERMAN-D. J. PENGELLEY-Index four orientable embeddings and case zero of the Heawood conjecture, J. Comb. Theory (B) ∼ August 1978.

    Google Scholar 

  5. J. L. GROSS-T. W. TUCKER-Generating all graph coverings by permutation voltage assignments.

    Google Scholar 

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Authors
  1. Jean-Claude Fournier
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Fournier, JC. (1979). Le théorème du coloriage des cartes [ex-conjecture de Heawood et conjecture des quatre couleurs]. In: Séminaire Bourbaki vol. 1977/78 Exposés 507–524. Lecture Notes in Mathematics, vol 710. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0069972

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  • DOI: https://doi.org/10.1007/BFb0069972

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09243-8

  • Online ISBN: 978-3-540-35340-9

  • eBook Packages: Springer Book Archive

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