G. Smith

Edge complexity of complete bipartite and complete multipartite graphs

We study edge complexity, the minimum Fourier $\ell^1/\ell^2$ ratio of a graph's adjacency matrix over cyclic vertex labelings. For $K_{m,n}$, with $1\leq m\leq n$, we reduce the problem to minimizing the Fourier $\ell^1$-norm of indicators of $m$-element subsets of $\mathbb Z_{m+n}$. We prove the sharp bound $\operato...