2 problems

Let $G$ be a planar graph and let $k$ be an integer. The $k$-recoloring graph $R_k(G)$ has vertices corresponding to proper $k$-colorings of $G$, with edges joining colorings that…

Let $G$ be a $d$-degenerate graph, and let $R_t(G)$ be the graph whose vertices are the proper $t$-colorings of $G$, with two colorings adjacent when they differ on one vertex. The…