4 problems

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

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…

Circular chromatic coefficient conjecture. The coefficients $c_\lambda(q)$ are palindromic and unimodal polynomials with non-negative integer coefficients. This extends and refines…

Let $\mathbf{a}$ be a circular area sequence, and let $\mathrm{X}_{\mathbf{a}}(\mathbf{x};q)$ be the corresponding chromatic symmetric function. Circular chromatic e-positivity con…