Skip to main content

200 years of graph theory — A guided tour

  • 1474 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 642)

Keywords

  • Binary Quantic
  • Opus Omnia
  • MObius Strip
  • Subgraph Homeomorphic
  • Domino Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahrens, W. Mathematische Unterhaltungen und Spiele, Leipzig, 1901.

    Google Scholar 

  2. Biggs, N. L., Lloyd, E. K. and Wilson, R. J., Graph Theory 1736–1936, Oxford Univ. Press, 1976.

    Google Scholar 

  3. Cauchy, A. — L., Recherches sur les polyèdres, J. Ecole Polytech. 9 (Cah. 16) (1813), 68–86 = Oeuvres (2), Vol. 1, 7–25.

    Google Scholar 

  4. Cayley, A., On the theory of the analytical forms called trees, Phil. Mag. (4) 13 (1857), 172–176 = Math. Papers. Vol. 3, 242–246.

    MathSciNet  Google Scholar 

  5. Cayley, A., On the analytical forms called trees, with application to the theory of chemical combinations, Rep. Brit. Assoc. Advance. Sci. 45 (1875), 257–305 = Math. Papers, Vol. 9, 427–460.

    Google Scholar 

  6. Cayley, A., On the colouring of maps, Proc. Roy. Geoq. Soc. 1 (1879), 259–261 = Math. Papers, Vol. 11, 7–8.

    Google Scholar 

  7. Clausen, T., De linearum tertii ordinis proprietatibus, Astron. Nachr. 21 (1844), col. 209–216.

    CrossRef  Google Scholar 

  8. Coupy, E., Solution d'un problème appartenant a la géométrie de situation, par Euler, Nouv. Ann. Math. 10 (1851), 106–119.

    Google Scholar 

  9. Coxeter, H. S. M., The four-color map problem, Math. Teacher 52 (1959), 283–289.

    MathSciNet  Google Scholar 

  10. Euler, L. Solutio problematis ad geometriam situs pertinentis. Comm. Acad. Sci. Imp. Petropol. 8 (1736), 128–140 = Opera Omnia (1), Vol. 7, 1–10.

    MATH  Google Scholar 

  11. Euler, L., Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita, Novi. Comm. Acad. Sci. Imp. Petropol. 4 (1752–3), 140–160 = Opera Omnia (1), Vol. 26, 94–108.

    Google Scholar 

  12. Euler, L., Solution d'une question curieuse qui ne paroit soumise à aucune analyse, Mém. Acad. Sci. Berlin 15 (1759), 310–337 = Opera Omnia (1), Vol. 7, 26–56.

    Google Scholar 

  13. Heawood, P. J., Map-colour theorem, Quart. J. Pure. Appl. Math. 24 (1890), 332–338.

    Google Scholar 

  14. Hierholzer, C., Ueber die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechnung zu umfahren, Math. Ann. 6 (1873), 30–32.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

  16. Kirkman, T. P., On the representation of polyedra, Phil. Trans. Roy. Soc. London 146 (1856), 413–418.

    CrossRef  Google Scholar 

  17. König, D., Theorie der endlichen und unendlichen Graphen, Akademische VerlagsgeseUschaft Leipzig, 1936. Reprinted by Chelsea, New York, 1950.

    Google Scholar 

  18. Kuratowski, K. Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271–283.

    MATH  Google Scholar 

  19. Legendre, A. M., Eléments de géométrie, Firmin Didot, Paris, 1794.

    Google Scholar 

  20. Lhuilier S., (abridged by J. D. Gergonne). Mémoire sur la polyédrométrie, Ann. Math. 3 (1812–13), 169–189.

    MathSciNet  Google Scholar 

  21. Listing, J. B., Vorstudien zur Topologie, Göttinger Studien 1 (1847), 811–875.

    Google Scholar 

  22. Listing, J. B., Der Census räumlicher Complexe oder Verallgemeinerung des Euler'schen Satzes von den Polyëdern, Abh. K. Ges. Wiss Göttingen Math. Cl. 10 (1861–2), 97–182.

    Google Scholar 

  23. Lucas, E., Récréations mathématiques, 4 vols. PulGauthier-Villars, Paris, 1882–94.

    Google Scholar 

  24. Maddison, I., Note on the history of the map-coloring problem, Bull. Amer. Math. Soc. 3 (1896–7), 257.

    CrossRef  MathSciNet  Google Scholar 

  25. Ringel, G., Map color theorem, Springer-Verlag, Berlin, 1974.

    CrossRef  MATH  Google Scholar 

  26. Rouse Ball, W. W., Mathematical recreations and essays (11th edn.), Macmillan, London, 1939.

    MATH  Google Scholar 

  27. Saalschütz, L., [Untitled], Schr. Phys. — Ökon. Ges. Königsberg Prussia 16 (1876), 23–24.

    Google Scholar 

  28. Sylvester, J. J., On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics, Amer. J. Math. 1 (1878), 64–125 = Math. Papers, Vol. 3, 148–206.

    CrossRef  MathSciNet  Google Scholar 

  29. Tait, P. G., On the colouring of maps. Proc. Roy. Soc. Edinburgh 10 (1878–80), 501–503, 729.

    Google Scholar 

  30. Vandermonde, A.-T., Remarques sur les problèmes de situation, Hist. Acad. Sci. (Paris) (1771), 566–674.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wilson, R.J. (1978). 200 years of graph theory — A guided tour. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070360

Download citation

  • DOI: https://doi.org/10.1007/BFb0070360

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

  • eBook Packages: Springer Book Archive