Skip to main content
SpringerLink
Log in

Decompositions of homology manifolds and their graphs

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

The graph of everyd-dimensional convex polytope isd-connected and contains a refinement of the complete graph ond+1 vertices. These two theorems are generalized to pseudomanifolds and to some very general decompositions of homology manifolds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Barnette,Graph theorems for manifolds, Israel J. Math.16 (1973), 62–72.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Barnette,Diagrams and Schlegel Diagrams, Combinatorial Structures and their Applications, Gordon and Breach, 1970.

  3. D. Barnette,Generalized combinatorial cells and facet splitting, Pacific J. Math.57 (1975), 33–45.

    MATH  MathSciNet  Google Scholar 

  4. S. Cairns,Introductory Topology, Ronald Press, 1961.

  5. V. Klee,A property of d-polyhedral graphs, J. Math. Anal. Appl.13 (1964), 1039–1042.

    MATH  MathSciNet  Google Scholar 

  6. D. Larman and P. Mani,On the existence of certain configurations within graphs and 1-skeletons of polytopes, Proc. London Math. Soc.20 (1970), 144–160.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. T. Sallee,Incidence graphs of polytopes, J. Combinatorial Theory2 (1967), 466–506.

    Article  MATH  MathSciNet  Google Scholar 

  8. E. Steinitz and H. Rademacher,Vorlesungen über die Theorie der Polyeder, Berlin, 1934.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, CA, USA

    David Barnette

Authors
  1. David Barnette
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by N.S.F. Grant #MPS-74-04830/1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barnette, D. Decompositions of homology manifolds and their graphs. Israel J. Math. 41, 203–212 (1982). https://doi.org/10.1007/BF02771721

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02771721

Keywords

Search

Navigation