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A Census of Planar Maps

  • W. T. Tutte (a1)
Extract

In the series of "Census" papers, of which this is the fourth, we attempt to lay the groundwork of an enumerative theory of planar maps (12, 13, 14). The maps concerned are rooted in the sense that some edge is fixed as the root, and a positive sense of description and right and left sides are specified for it. This device simplifies the theory by ruling out the possibility of a map being symmetrical.

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References
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1. Berge, C., Théorie des graphes et ses applications (Paris, 1958).
2. Bouwkamp, C. J., On the dissection of rectangles into squares, I—III, Konink. Nederland. Akad. Wetenschap. Proc, Jfi (1946), 1176-1188 and 50 (1947), 5878.
3. Bouwkamp, C. J., Duijvestijn, A. J. W., and Medema, P., Tables relating to simple squared, rectangles of orders nine through fifteen (Eindhoven, 1960).
4. Brooks, R. L., Smith, C. A. B., Stone, A. H., and Tutte, W. T., The dissection of rectangles into squares, Duke Math. J., 7 (1940), 312340.
5. Heawood, P. J., Map-colour theorem, Quart. J. Math., 24 (1890), 332338.
6. Kônig, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936, and New York (1950).
7. Lefschetz, S., Algebraic topology, A. M. S. Colloquium Publications 27 (1942).
8. Lefschetz, S., Introduction to topology (Princeton, 1949).
9. M. H. A. Newman, , Elements of the topology of plane sets of points (Cambridge, 1939).
10. Ore, O., Theory of graphs, A.M.S. Colloquium Publications 88 (1962).
11. Rouse Ball, W. W., Mathematical recreations and essays (London, 1940).
12. Tutte, W. T., A census of planar triangulations, Can. J. Math., 14 (1962), 2138.
13. Tutte, W. T., A census of Hamiltonian polygons, Can. J. Math., 14 (1962), 402417.
14. Tutte, W. T., A census of slicings, Can. J. Math., 14 (1962), 708722.
15. Whittaker, E. T. and Watson, G. N., A course of modern analysis (Cambridge, 1940).
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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