Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T17:46:05.686Z Has data issue: false hasContentIssue false
  • English
  • Français

On acyclic simplicial complexes

Published online by Cambridge University Press:  26 February 2010

Frank Harary  and
Edgar M. Palmer
Frank Harary
Affiliation:
University of Michigan
Edgar M. Palmer
Affiliation:
University College, London
Get access

Extract

The higher dimensional concepts corresponding to trees are developed and studied. In order to enumerate these 2-dimensional structures called 2-trees, a dissimilarity characteristic theory is investigated. By an appropriate application of certain combinatorial techniques, generating functions are obtained for the number of 2-trees. These are specialized to count those 2-trees embeddable in the plane, thus providing a new approach to the old problem of determining the number of triangulations of a polygon.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 1 , June 1968 , pp. 115 - 122
Copyright
Copyright © University College London 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Brown, W. G., “Enumeration of triangulations of the disk”, Proc. London Math Soc, 14 (1964), 746–768.CrossRefGoogle Scholar
2.Brown, W. G., “Historical note on a recurrent combinatorial problem”, Amer. Math. Monthly, 72 (1965), 973–977.CrossRefGoogle Scholar
3.Harary, F., “The number of linear, directed, rooted, and connected graphs”, Trans. Amer Math. Soc., 78 (1955), 445–463.CrossRefGoogle Scholar
4.Harary, F., “Combinatorial problems in graphical enumeration”, Chapter 6 in Applied Combinatorial Mathematics, Beckenbach, E. F., ed. (New York, Wiley, 1964), 185–217.Google Scholar
5.Harary, F., A seminar on graph theory (New York, Holt, Rinehart and Winston, 1967), 1–41.Google Scholar
6.Harary, F. and Norman, R. Z., “Dissimilarity characteristic theorems for graphs”, Proc. Amer Math. Soc., 11 (1960), 332–334.CrossRefGoogle Scholar
7.Harary, F. and Prins, G., “The number of homeomorphically irreducible trees and other species”, Acta Math., 101 (1959), 141–162.CrossRefGoogle Scholar
8.König, D., Theorie der endlichen und unendlichen Graphen (Leipzig, 1936; reprinted New York, Chelsea, 1950).Google Scholar
9.Otter, R., “The number of trees”, Ann. of Math., 49 (1948), 583–599.CrossRefGoogle Scholar
10.Polya, G., “Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen”, Acta Math., 68 (1937), 145–254.CrossRefGoogle Scholar