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Journal of Geometry

, Volume 8, Issue 1–2, pp 171–186 | Cite as

S-functions for graphs

  • Rudolf Halin
Article

Abstract

S-functions are mappings from the class of finite graphs into the set of integers, such that certain formal conditions are fulfilled which are shared by the chromatic number, the vertex-connectivity, and the homomorphism-degree. The S-functions form a complete lattice (with respect to their natural partial order). The classes of graphs with values <n under some S-function are studied from a general point of view, and uncountably many S-functions are constructed. Further for every n≥5 a non-trivial base-element of
(see K. WAGNER [7]) is constructed.

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References

  1. [1]
    Erdös, P. and Pósa, L.: On independent circuits contained in a graph. Canad.J.Math. 17 (1965), 347–352.Google Scholar
  2. [2]
    Hadwiger, H.: über eine Klassifikation der Strecken-komplexe. Vierteljahresschr. Naturforsch. Ges. Zürich 88 (1943), 133–142.Google Scholar
  3. [3]
    Halin, R.: Zur Klassifikation der endlichen Graphen nach H. Hadwiger und K. Wagner. Math. Ann. 172 (1967), 46–78.Google Scholar
  4. [4]
    Mader, W.: Homomorphieeigenschaften und mittlere Kanten-dichte von Graphen. Math. Ann. 174 (1967), 265–268.Google Scholar
  5. [5]
    Ore, O.: Theory of graphs. Providence 1962.Google Scholar
  6. [6]
    Wagner, K.: über eine Eigenschaft der ebenen Komplexe. Math. Ann. 114 (1937), 570–590.Google Scholar
  7. [7]
    Wagner, K.: Bemerkungen zu Hadwigers Vermutung. Math. Ann. 141 (1960), 433–451.Google Scholar
  8. [8]
    Wagner, K.: Beweis einer Abschwächung der Hadwiger-Vermutung. Math. Ann. 153 (1964), 139–141.Google Scholar
  9. [9]
    Wagner, K.: Graphentheorie. Bibliographisches Institut, Mannheim 1970.Google Scholar
  10. [10]
    Wagner, K. und Halin, R.: Homomorphiebasen von Graphenmengen. Math. Ann. 147 (1962), 126–142.Google Scholar

Copyright information

© Birkhäuser Verlag 1976

Authors and Affiliations

  • Rudolf Halin
    • 1
  1. 1.Mathematisches Seminar der Universität2 Hamburg 13

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