We show that there is no subexponential time algorithm for computing the exact solution of the maximum independent set problem in d-regular graphs, unless ETH fails. We expand our method to show that it helps to provide lowerbounds for other covering problems such as vertex cover and clique. We utilize the construction to show the NP-hardness of MIS on 5-regular planar graphs, closing the exact complexity status of the problem on regular planar graphs.

中文翻译：

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关于正则图上MIS细粒度复杂性的注释

我们证明，除非ETH失败，否则没有用于计算d正则图中最大独立集问题的精确解的次指数时间算法。我们扩展了方法，以表明它有助于为其他覆盖问题（例如顶点覆盖和团）提供下限。我们利用该构造在5个规则平面图上显示MIS的NP硬度，从而关闭了问题在规则平面图上的确切复杂性状态。