Matthew Kwan and Yuval Wigderson showed that for an infinite family of graphs, the Lov\'asz number gives an upper bound of $O(n^{ 3/4})$ for the size of an independent set (where $n$ is the number of vertices), while the weighted inertia bound cannot do better than $\Omega(n)$. Here we point out that there is an infinite family of graphs for which the Lov\'asz number is $\Omega(n^{ 3/4})$, while the unweighted inertia bound is $O(n^{ 1/2})$.
Categories: math.CO