3 problems

Let $G=(V,E)$ be a graph with maximum degree $\Delta$. A proper $q$-coloring assigns one of $q$ colors to each vertex so that adjacent vertices receive distinct colors. The single-…

Davies–Perkins quantitative conjecture. For every $1\leq k\leq(1-\delta)n\alpha_c(\Delta)$, the $\epsilon$-mixing time of this chain is

Let $G=(V,E)$ be a bipartite graph, and for parameters $q$ and $bc$ define the adjacency-rank polynomial … where $\operatorname{rk}_2(S)$ is the rank over $\mathbb{F}_2$ of the adj…