Maximum star densities

Abstract

Given an integer $k \geq 2$ and a real number $γ\in [0, 1]$, which graphs of edge density $γ$ contain the largest number of $k$-edge stars? For $k=2$ Ahlswede and Katona proved that asymptotically there cannot be more such stars than in a clique or in the complement of a clique (depending on the value of $γ$). Here we extend their result to all integers $k\ge 2$.

third version addresses changes arising from the referee reports