How Is a Graph like a Manifold?

  title={How Is a Graph like a Manifold?},
  author={VICTOR W. GUILLEMIN and Tara S. Holm and A BSTRACT},
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… CONTINUE READING