How is a graph like a manifold-sysj.pdf
In this article, we discuss some classical problems in combinatorics
which can be solved by exploiting analogues between graph theory and the the
ory of manifolds. One well-known example is the McMullen conjecture, which
was settled twenty years ago by Richard Stanley by interpreting certain combina
torial 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.