Pacific Journal of Mathematics

Quotients of complete graphs: revisiting the Heawood map-coloring problem.

Jonathan L. Gross and Thomas W. Tucker

Article information

Source
Pacific J. Math., Volume 55, Number 2 (1974), 391-402.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102910975

Mathematical Reviews number (MathSciNet)
MR0389635

Zentralblatt MATH identifier
0306.55001

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Citation

Gross, Jonathan L.; Tucker, Thomas W. Quotients of complete graphs: revisiting the Heawood map-coloring problem. Pacific J. Math. 55 (1974), no. 2, 391--402. https://projecteuclid.org/euclid.pjm/1102910975


Export citation

References

  • [1] S. R. Alpert and J. L. Gross, Components of branched coverings of current graphs, in preparation.
  • [2] J. L. Gross, Voltage graphs, Discrete Math., in press.
  • [3] J. L. Gross and S. R. Alpert, Branchedcoverings of graph imbeddings, Bull. Amer. Math. Soc, 79 (1973), 942-945.
  • [4] J. L. Gross and S. R. Alpert, The topological theory of current graphs, J. Combinatorial Theory, to appear.
  • [5] J. L. Gross and T. W. Tucker, Generatingall graph coverings by voltage dis- tributions, in preparation.
  • [6] W. Gustin, Orientable embeddings of Cayley graphs, Bull. Amer. Math. Soc, 69 (1963), 272-275.
  • [7] F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, 1969.
  • [8] P. J. Heawood, Map color theorem, Quart. J. Math., 24 (1890), 332-338.
  • [9] L. Heffter, Uber das Problem der Nachbargebiete, Math, Ann., 38 (1891), 477-508.
  • [10] A. B. Kempe, On the geographical problem of fourcolors, Amer. J. Math., 2 (1879), 193-204.
  • [11] W. S. Massey, Algebraic Topology:An Introduction, Harcourt, Brace & World, New York, 1967.
  • [12] J. Mayer, Le probleme des regions voisines sur les surfaces closes orientables, J. Combinatorial Theory, 6 (1969), 177-195.
  • [13] C. M. Terry, L. R. Welch, and J. W. T. Youngs, The genus of K12s, J. Combinatorial Theory, 2 (1967), 43-60.
  • [14] C. M. Terry, Solution of the Heawood map-coloring problem--case 4, J. Combinatorial Theory, 8 (1970), 170-174.
  • [15] G. Ringel, Bestimmungder Maximalzahlder Nachbargebiete aufnichtorientier- baren Flachen, Math. Ann., 127 (1954), 181-214.
  • [16] G. Ringel, Uber das Problem der Nachbargebiete auf orientierbaren Flachen, Abh. Math. Sem. Univ. Hamburg, 25 (1961), 105-127.
  • [17] G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem, Proc. Nat. Acad. Sci. U.S.A., 60 (1968), 438-445.
  • [18] G. Ringel and J. W. T. Youngs, Lbsung des Problems der Nachbargebiete auf orientierbarenFlachen, Archiv der Mathematik, 20 (1969), 190-201.
  • [19] G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem--case 11, J. Combinatorial Theory, 7 (1969), 71-93.
  • [20] G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem--case 2, J. Combinatorial Theory, 7 (1969), 342-352.
  • [21] G. Ringel and J. W. T. Youngs, Solution of the Heawood map-coloring problem--case 8, J. Combinatorial, Theory, 7 (1969), 353-363.
  • [22] J. W. T. Youngs, The Heawood Map-coloringConjecture, Graph Theory and Theoretical Physics, Academic Press, London, 1967, pp. 313-354.
  • [23] J. W. T. Youngs, Solution of the Heawood map-coloring problem--cases 3, 5, 6 and 9, J. Combinatorial Theory, 8 (1970), 175-219.
  • [24] J. W. T. Youngs, Solution of the Heawood map-coloring problem--cases, 1, 7, and
  • [10] J. Combinatorial Theory, 8 (1970), 220-231.
  • [25] M. Jungerman, Ph. D. dissertation, University of California at Santa Cruz, 1974.