4 problems

Let $G$ be a graph. Consider its number of spanning trees, its number of acyclic orientations, and its number of totally cyclic orientations. Welsh–Merino conjecture. The number of…

Two-orientation deletability conjecture. For every cubic $3$-edge-connected graph $G$, there exist two strongly connected orientations $D_1$ and $D_2$ of $G$ such that for every ve…

The Atiyah-Bott-Shapiro orientation $mathrm{MSpin}to mathrm{bo}$ is known to admit a spectrum-level splitting, and $mathrm{MString}to mathrm{tmf}$ is the Ando-Hopkins-Rezk orient…

Cover inequality. Then