7 problems

Let $m$ be the number of subsets, let $p$ be the inclusion probability, and let $n$ be the number of elements. Write $\operatorname{val}_{\mathrm{GR}}$ for the value produced by th…

Let $m$ be the number of subsets, let $p$ be the inclusion probability, and let $n$ be the number of elements. Write $\operatorname{val}_{\mathrm{GR}}$ for the value produced by th…

Let $m$ be the number of subsets, let $p$ be the inclusion probability, and let $n$ be the number of elements. Write $\operatorname{val}_{\mathrm{GR}}$ for the value produced by th…

Good-function conjecture. If

De Klerk–Dobre conjecture. For every circulant TSP instance,

Six-fifths conjecture. If $x\in\mathrm{LP}(G)$, then $\frac{6}{5}x$ dominates a convex combination of 2-edge-connected multigraphs of $G$. Equivalently,

Let ${\cal G}$ be any proper minor-closed family of graphs. The constant-congestion integrality-gap conjecture. The integrality gap of the flow LP for maximum edge-disjoint paths i…