The reconfiguration graph $R_k(G)$ for the $k$-colorings of a graph $G$ has as vertex set the set of all possible $k$-colorings of $G$ and two colorings are adjacent if they differ in the color of exactly one vertex of $G$. Let $d, k \geq 1$ be integers such that $k \geq d+1$. We prove that for every $\epsilon > 0$ and every graph $G$ with $n$ vertices and maximum average degree $d - \epsilon$, $R_k(G)$ has diameter $O(n(\log n)^{d - 1})$. This significantly strengthens several existing results.

翻译：图表$G$(G) 的重新配置图 $R_k(G)$-彩色的重新配置图 $G$(K$-彩色) 作为顶点设置了所有可能的$G$(K$-彩色)和两个彩色的套件,如果这些彩色的颜色与1G$(G美元)的正好颜色不同的话,这些彩色和彩色是相邻的。让 k\geq 1美元为整数,以至 $k\geq d+1美元。我们证明,每张$ > 0美元和每张图$$(G),以美元为顶点和最高平均价$d -\ epslon$, $R_k(G) 美元具有直径$(n(glog n) d - 1}。这大大加强了现有的几项结果。