Glauber dynamics for the hard-core model on bounded-degree H-free graphs

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' >0, with higher 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, the mixing time is O (n 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, depending on H and the maximum degree of G.