# The four color proof suffices

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## Conclusion

Since no one else has communicated any other errors in the published unavoidability proof since 1976 we assume that a misunderstanding of the nature of Schmidt’s work was the source of those rumors that seem to have stimulated so much new interest in our work. We would certainly appreciate independent verification of the remaining 60 percent of our unavoidability proof and would be grateful for any information on further bookkeeping (or other) errors whenever such are found.* We have written computer programs preparatory to a thorough com puter verification of all of the material in the microfiche supplements. When this is completed we plan to publish (entirely on paper rather than on microfiche cards) an entire emended version of our original proof including the*q*-positive bookkeeping. At first thought one might think that we would miss the pleasures of discussing the latest rumors with our colleagues returning from meetings but further consideration leads us to believe that facts have never stopped the propagation of a good rumor and so nothing much will change.

## Keywords

Initial Charge Central Versus Independent Verification Connected Planar Graph Planar Triangulation## Preview

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## References

- 1.F. Allaire, Another proof of the Four Colour Theorem I, Proc. of the Seventh Manitoba Conference on Numerical Mathematics and Computing, Univ. Manitoba, Winnipeg, Man., 1977, pp. 3–72.Google Scholar
- 2.F. Allaire and E. R. Swart, A systematic approach to the determination of reducible configurations in the four-color conjecture, J. Combinatorial Theory(B)
*25*(1978), pp. 339–362.CrossRefzbMATHMathSciNetGoogle Scholar - 3.K. Appel and W. Haken, Every planar map is four colorable Part I: Discharging, Illinois J. Math.,
*21*(1977), pp. 429–490.zbMATHMathSciNetGoogle Scholar - 4.K. Appel, W. Haken and J. Koch, Every planar map is four colorable Part II: Reducibility, Illinois J. Math.
*21*(1977), pp. 491–567.zbMATHMathSciNetGoogle Scholar - 5.K. Appel and W. Haken, The solution of the four-color-map problem, Scientific American, September 1977, pp. 108–121.Google Scholar
- 6.G. D. Birkhoff, The reducibility of maps, Amer. J. Math.,
*35*(1913), pp. 114–128.CrossRefMathSciNetGoogle Scholar - 7.K. Dürre, H. Heesch and F. Miehe, Eine Figurenliste zur chromatischen Reduktion, Technische Universität Hannover, Institut für Mathematik, 1977, Nr. 73.Google Scholar
- 8.H. Heesch, Untersuchungen zum Vierfarbenproblem, B-I-Hochschulscripten 810/810a/810b, Bibliographisches Institut, Mannheim/Vienna/Zurich, 1969.Google Scholar
- 9.H. Heesch, Chromatic reduction of the triangulations T
_{e}, e = e_{5}+ e_{7}, J. Combinatorial Theory,*13*(1972), pp. 46–53.CrossRefzbMATHMathSciNetGoogle Scholar - 10.A. B. Kempe, On the geographical problem of the four colors, Amer. J. Math.,
*2*(1879), pp. 193–200.CrossRefMathSciNetGoogle Scholar - 11.U. Schmidt, Überprüfung des Beweises für den Vierfarbensatz. Diplomarbeit, Technische Hochschule Aachen, 1982.Google Scholar
- 12.W. Stromquist, Some aspects of the four color problem, Ph.D. Thesis, Harvard University, 1975.Google Scholar
- 13.W. Tutte and H. Whitney, Kempe chains and the four color problem, Utilitas Math.
*2*(1972), pp. 141–281.MathSciNetGoogle Scholar