4 problems

Kang–Kim–Liu conjecture. Under this hypothesis,

Subdivision conjecture. Every graph has a subdivision obtained by multiplying subdividing its edges such that the resulting graph belongs to $\mathcal{G}_s^s$.

Let $K_F$ be the graph under consideration, let $\ell_e$ denote the length of the subdivided path corresponding to an edge $e$ of $K_F$, and let $\ell^*$ be the threshold in the co…

Let $G$ be a finite graph, and let $G^{1/m}$ be the graph obtained by replacing every edge of $G$ by a path of length $m$ through new vertices. A graph is locatable if the cop has…