Le théorème du coloriage des cartes (ex-conjecture de Heawood et conjecture des quatre couleurs)

Jean-Claude Fournier

Séminaire Bourbaki (1977-1978)

  • Volume: 20, page 41-64
  • ISSN: 0303-1179

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Fournier, Jean-Claude. "Le théorème du coloriage des cartes (ex-conjecture de Heawood et conjecture des quatre couleurs)." Séminaire Bourbaki 20 (1977-1978): 41-64. <http://eudml.org/doc/109927>.

@article{Fournier1977-1978,
author = {Fournier, Jean-Claude},
journal = {Séminaire Bourbaki},
keywords = {map coloring; closed surfaces; four colour conjecture; representation of graphs; Heawood conjecture; Hadwiger conjecture},
language = {fre},
pages = {41-64},
publisher = {Springer-Verlag},
title = {Le théorème du coloriage des cartes (ex-conjecture de Heawood et conjecture des quatre couleurs)},
url = {http://eudml.org/doc/109927},
volume = {20},
year = {1977-1978},
}

TY - JOUR
AU - Fournier, Jean-Claude
TI - Le théorème du coloriage des cartes (ex-conjecture de Heawood et conjecture des quatre couleurs)
JO - Séminaire Bourbaki
PY - 1977-1978
PB - Springer-Verlag
VL - 20
SP - 41
EP - 64
LA - fre
KW - map coloring; closed surfaces; four colour conjecture; representation of graphs; Heawood conjecture; Hadwiger conjecture
UR - http://eudml.org/doc/109927
ER -

References

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  1. [1] A.B. Kempe - On the geographical problem of the four colours, Amer. J. Math., 2(1879), 193-200. MR1505218
  2. [2] P.J. Heawood - Map colour theorem, Quart. J. Math., 24(1890), 332-338. JFM22.0562.02
  3. [3] G.D. Birkhoff - The reducibility of maps, Amer. J. Math., 35(1913), 114-128. MR1506176JFM44.0568.01
  4. [4] H. Lebesgue - Quelques conséquences simples de la formule d'Euler, J. de Math., 9, Sér. 19 (1940), 27-43. Zbl0024.28701MR1903JFM66.0736.03
  5. [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. Zbl0077.36802MR86306
  6. [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. Zbl0071.17701MR81467
  7. [17] H. Hadwiger - Ungelöste Probleme, Element. Math., 13(1958), 127-128. 
  8. [8] K. Wagner - Bemerkungen zur Hadwigers Vermutung, Math. Annalen, 141(1960), 433- 451. Zbl0096.17904MR121309
  9. [9] J. W . T . Youngs - Minimal imbeddings and the genus of a graph, J. Math. Mech., 12(1963), 303-314. Zbl0109.41701MR145512
  10. [10] W. Gustin - Orientable embedding of Cayley graphs, Bull. Amer. Math. Soc., 69 (1963), 272-275. Zbl0118.18805MR145506
  11. [11] O. Ore - The four-color problem, Pure and Applied Maths., 27, Acad. PressNew York-London, 1967. Zbl0149.21101MR216979
  12. [12] J. W. T . Youngs - The Heawood map-colouring conjecture, Chapter 12 in Graph Theory and Theoretical physics (F. Harary ed.), Acad. PressNew York- London, 1967, 313-354. Zbl0205.54402MR236059
  13. [13] W. Mader - Homomorphiesätze für Graphen, Math. Annalen, 178(1968), 154-168. Zbl0165.57401MR229550
  14. [14] H. Heesch - Untersuchungen zum Vierfarbenproblem, B.I. Hochschulskripten 810/810a/810b, Bibliographische InstituteMannheim-Vienna-Zürich, 1969. Zbl0187.20904MR248048
  15. [15] N. Biggs - Classification of complete maps on orientable surfaces, Rend. Matematica (VI), 4(1971), 645-655. Zbl0235.05104MR321773
  16. [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. Zbl0244.05103MR321774
  17. [17] W. Tutte - H. Whitney - Kempe chains and the four color problem, Utilitas Mathemetica, 2(1972), 241-281. Zbl0253.05120MR309782
  18. [18] G. Ringel - Map color theorem, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Band 209, Springer-Verlag, Berlin-New York, 1974, 191 pages. Zbl0287.05102MR349461
  19. [19] M. Jungerman - Orientable triangular embeddings of K18 - K3 and K13 - K3 , J. Comb. Theory (B),16(1974), 293-294. Zbl0277.05108MR342421
  20. [20] J.L. Gross - Voltage graphs, Discrete Mathematics, 9(1974), 239-246. Zbl0286.05106MR347651
  21. [21] J.L. Gross - T.W. Tucker - Quotients of complete graphs : revisiting the Heawood map-colouring problem, Pacific J. Math., 55(1974), 391-402. Zbl0306.55001MR389635
  22. [22] M. Jungerman - The genus of K - K2 , J. Comb. Theory (B),18(1975), 53-58. Zbl0317.05104MR366718
  23. [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. Zbl0306.05105MR406848
  24. [24] S.R. Alpert- J.L. Gross - Components of branched coverings of current graphs, J. Comb. Theory (B), 20(1976), 283-303. Zbl0298.05107MR419278
  25. [25] G. Ringel - The combinatorial map color theorem, J. Graph Theory1 (Summer 1977), 141-155. Zbl0386.05030MR444509
  26. [26] K. Appel- W. Haken - Every planar map is four colorable, Part I : discharging, Part II : reducibility, Illinois J. Math. MR1025335
  27. [27] K. Appel- W. Haken- J. Mayer - Triangulations à V5 séparés dans le problème des quatre couleurs. Zbl0344.05113
  28. [28] R. Ringel - Non-existence of graph embeddings, Theory and Applications of graphs, Springer-Verlag. Zbl0398.05031
  29. [29] M. Jungerman - D.J. Pengelley - Index four orientable embeddings and case zero of the Heawood conjecture, J. Comb. Theory (B) ∼ August 1978. Zbl0331.05102
  30. [30] J.L. Gross - T.W. Tucker - Generating all graph coverings by permutation voltage assignments. Zbl0375.55001

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