6 problems

Morell and Skutella's conjecture. Any fractional flow $(x_e)_{e\in E}$ can be expressed as a convex combination of unsplittable flows $(y_e)_{e\in E}$ satisfying both bounds. The s…

Let $S$ be a source set in the directed hypercube with separation distance $r$. Consider a flow network with unit edge capacities and vertex capacities $r^2$. Flow-capacity conject…

Robust flow gap conjecture. For any $\Gamma\in\mathbb{N}$, the inequalities

Priority-queue implementation conjecture. Such an algorithm can be implemented with $O(n)$ queries to a priority queue.

Loose weighted-web conjecture. A loose weighted web is linkable.

Orthogonal web-flow conjecture. In every weighted web there exists a web-flow $f$ and an $A$-$B$ separating set orthogonal to $f$.