How is a graph like a manifold?

Details How is a graph like a manifold? How is a graph like a manifold?

2002-06-10

arxiv.org/abs/math/0206103v1

Mathematics

Combinatorics

36 pages, 17 figures

Scientific paper

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.

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