Journal of Geometry

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

S-functions for graphs

  • Rudolf Halin


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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Copyright information

© Birkhäuser Verlag 1976

Authors and Affiliations

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

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