Extension Complexity of Independent Set Polytopes
  We exhibit an $n$-node graph whose independent set polytope requires extended formulations of size exponential in $\Omega(n/\log n)$. Previously, no explicit examples of $n$-dimensional $0/1$-polytopes were known with extension complexity larger than exponential in $\Theta(\sqrt{n})$. Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth. 
Mika G\"o\"os, Rahul Jain, Thomas Watson
cs.CC cs.DM math.CO