# Atserias, Albert

## Vertex Cover Integrality Gap ★★

Author(s): Atserias

\begin{conjecture} For every $\varepsilon > 0$ there is $\delta > 0$ such that, for every large $n$, there are $n$-vertex graphs $G$ and $H$ such that $G \equiv_{\delta n}^{\mathrm{C}} H$ and $\mathrm{vc}(G) \ge (2 - \varepsilon) \cdot \mathrm{vc}(H)$. \end{conjecture}

Keywords: counting quantifiers; FMT12-LesHouches