How is a graph like a manifold?

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In this article, we discuss some classical problems in combinatorics which can be solved by exploiting analogues between graph theory and the theory of manifolds. One well-known example is the McMullen conjecture, which was settled twenty years ago by Richard Stanley by interpreting certain combinatorial invariants of convex polytopes as the Betti numbers of a complex projective variety. Another example is the classical parallel redrawing problem, which turns out to be closely related to the problem of computing the second Betti number of a complex compact $(\C^*)^n$-manifold.
36 pages, 17 figures

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Combinatorics, 05C99

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http://salesiana.dossiersoluciones.com/handle/123456789/64272

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206103
 http://arxiv.org/abs/math/0206103

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arXiv