5 problems

Let $F$ be a family of arcs on a circle, and let $\omega(F)$ be the maximum size of a set of pairwise intersecting arcs in $F$. Tucker's coloring conjecture. The family $F$ can be…

Rzk{a}.{z}ewski's conjecture. Locally interval graphs are exactly circular-arc graphs.

Max-load extension conjecture. Under these assumptions,

Let ${\boldsymbol\nu}$ determine a circular vertical-strip digraph, let $\Gamma_{\boldsymbol\nu}$ be its underlying digraph, and let $O_\ast(\Gamma_{\boldsymbol\nu})$ denote the or…

Let $\Gamma$ be a circular unit arc digraph, and let $H$ be a graph obtained from $\Gamma$ by marking $k$ corner edges strict. Strict-corner difference conjecture. Then … is…