The hard-core model has as its configurations the independent sets of some graph instance $G$. The probability distribution on independent sets is controlled by a `fugacity' $\lambda>0$, with higher $\lambda$ leading to denser configurations. We investigate the mixing time of Glauber (single-site) dynamics for the hard-core model on restricted classes of bounded-degree graphs in which a particular graph $H$ is excluded as an induced subgraph. If $H$ is a subdivided claw then, for all $\lambda$, the mixing time is $O(n\log n)$, where $n$ is the order of $G$. This extends a result of Chen and Gu for claw-free graphs. When $H$ is a path, the set of possible instances is finite. For all other $H$, the mixing time is exponential in $n$ for sufficiently large $\lambda$, depending on $H$ and the maximum degree of $G$.

翻译：硬核模型以其配置为某图实例 $G$ 的独立集。独立集上的概率分布由“逸度” $\lambda>0$ 控制，较高的 $\lambda$ 导致更密集的配置。我们研究在受限的有界度图类上硬核模型的格劳伯（单站点）动力学的混合时间，其中特定图 $H$ 被排除作为诱导子图。若 $H$ 是细分爪图，则对所有 $\lambda$，混合时间为 $O(n\log n)$，其中 $n$ 是 $G$ 的阶。这扩展了 Chen 和 Gu 关于无爪图的结果。当 $H$ 是路径时，可能实例的集合是有限的。对于所有其他 $H$，当 $\lambda$ 足够大时（取决于 $H$ 和 $G$ 的最大度），混合时间关于 $n$ 呈指数级增长。