4 problems

For a finite graph $G$, let $\mathcal C_k(G)$ be its coloring graph. Finite coloring-graph determination conjecture. There exists a function…

For a finite graph $G$, let $\mathcal C_k(G)$ be its coloring graph for $k\geq 1$, and let $\pi_G^{(H)}$ count induced copies of a graph $H$ in these coloring graphs. Coloring-grap…

Let $G_1$ and $G_2$ be graphs. For each vertex $v$, let $\rho_{r_v^{(2)}}(k)$ denote the corresponding restrained chromatic polynomial, and consider the multiset of these polynomia…

Let $G_1$ and $G_2$ be graphs, and let $\pi_{G_i}^{(P_2)}(k)$ denote their chromatic pairs polynomials and $\pi_{G_i}(k)$ their chromatic polynomials. Chromatic-pairs refinement co…