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Manifolds associated with (2)n+1-colored regular graphs

  • Zhiqiang Bao EMAIL logo and Zhi Lü
Published/Copyright: January 19, 2012

Abstract.

In this article we describe a canonical way to expand a certain kind of (2)n+1-colored regular graphs into closed n-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial n-manifold can be obtained in this way. When n3, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a (2)n+1-colored regular graph admits an n-skeletal expansion, then it is realizable as the induced graph of an (n+1)-dimensional closed (2)n+1-manifold.

Received: 2009-09-07
Revised: 2010-02-26
Published Online: 2012-01-19
Published in Print: 2012-January

© 2012 by Walter de Gruyter Berlin Boston

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