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Graph theorems for manifolds

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Abstract

Two basic theorems about the graphs of convex polytopes are that the graph of ad-polytope isd-connected and that it contains a refinement of the complete graph ond+1 vertices. We obtain generalizations of these theorems, and others, for manifolds. We also supply some details for a proof of the lower bound inequality for manifolds.

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Authors and Affiliations

  1. University of California, Davis, Davis, California, USA

    David Barnette

Authors
  1. David Barnette
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Additional information

Research supported by NSF Grants GP 8470 and GP 19221.

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Barnette, D. Graph theorems for manifolds. Israel J. Math. 16, 62–72 (1973). https://doi.org/10.1007/BF02761971

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  • DOI: https://doi.org/10.1007/BF02761971

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