McCuaig (2001, Brace Generation, J. Graph Theory 38: 124-169) proved a generation theorem for braces, and used it as the principal induction tool to obtain a structural characterization of Pfaffian braces (2004, P{\'o}lya's Permanent Problem, Electronic J. Combinatorics 11: R79). A brace is minimal if deleting any edge results in a graph that is not a brace. From McCuaig's brace generation theorem, we derive our main theorem that may be viewed as an induction tool for minimal braces. As an application, we prove that a minimal brace of order $2n$ has size at most $5n-10$, when $n \geq 6$, and we provide a complete characterization of minimal braces that meet this upper bound. A similar work has already been done in the context of minimal bricks by Norine and Thomas (2006, Minimal Bricks, J. Combin. Theory Ser. B 96: 505-513) wherein they deduce the main result from the brick generation theorem due to the same authors (2007, Generating Bricks, J. Combin. Theory Ser. B 97: 769-817).

中文翻译：

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最小括号

McCuaig (2001, Brace Generation, J. Graph Theory 38: 124-169) 证明了大括号的生成定理，并用它作为主要归纳工具来获得 Pfaffian 大括号的结构特征 (2004, P{\'o}lya's永久问题，Electronic J. Combinatorics 11：R79）。如果删除任何边导致图形不是大括号，则大括号是最小的。从 McCuaig 的括号生成定理，我们推导出我们的主要定理，可以将其视为最小括号的归纳工具。作为一个应用，我们证明了 $2n$ 阶的最小括号的大小最多为 $5n-10$，当 $n \geq 6$ 时，我们提供了满足这个上限的最小括号的完整特征。Norine 和 Thomas（2006 年，Minimal Bricks, J. Combin. Theory Ser. B 96）已经在最小积木的背景下进行了类似的工作：