We calculate exponential growth constants [Formula: see text] and [Formula: see text] describing the asymptotic behavior of spanning forests and connected spanning subgraphs on strip graphs, with arbitrarily great length, of several two-dimensional lattices, including square, triangular, honeycomb, and certain heteropolygonal Archimedean lattices. By studying the limiting values as the strip widths get large, we infer lower and upper bounds on these exponential growth constants for the respective infinite lattices. Since our lower and upper bounds are quite close to each other, we can infer very accurate approximate values for these exponential growth constants, with fractional uncertainties ranging from [Formula: see text] to [Formula: see text]. We show that [Formula: see text] and [Formula: see text] are monotonically increasing functions of vertex degree for these lattices.

中文翻译：

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二维格上跨越森林和连通跨越子图的渐近行为

我们计算指数增长常数 [公式：见正文] 和 [公式：见正文] 描述跨越森林的渐近行为和带状图上的连接跨越子图，具有任意大的长度，包括正方形、三角形、蜂窝和某些异多角阿基米德晶格。通过研究带材宽度变大时的极限值，我们推断出相应无限晶格的这些指数增长常数的下限和上限。由于我们的下限和上限非常接近，我们可以推断出这些指数增长常数的非常准确的近似值，分数不确定性范围从 [公式：参见文本] 到 [公式：参见文本]。我们证明了 [公式：见正文] 和 [公式：