Graph domain variables and constraints are an extension of constraint programming introduced by Dooms et al. This approach had been further investigated by Fages in its PhD thesis. On the other hand, Beldiceanu et al. presented a generic filtering scheme for global constraints based on graph properties. This scheme strongly relies on the computation of graph properties' bounds and can be used in the context of graph domain variables and constraints with a few adjustments. Bounds of MIN_NCC and MAX_NCC had been defined for the graph-based representation of global constraint for the path_with_loops graph class. In this note, we generalize those bounds for graph domain variables and for any graph class. We also provide a filtering scheme for any graph class and arbitrary bounds.

中文翻译：

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MIN_NCC和MAX_NCC的界限以及图域变量的过滤方案

图域变量和约束是Dooms等人引入的约束编程的扩展。Fages在其博士论文中对此方法进行了进一步的研究。另一方面，Beldiceanu等。提出了一种基于图属性的全局约束通用过滤方案。该方案强烈依赖于图形属性边界的计算，并且可以在图形域变量和约束条件下进行一些调整来使用。已经为path_with_loops图类的全局约束的基于图的表示形式定义了MIN_NCC和MAX_NCC的界限。在本说明中，我们概括了图域变量和任何图类的界限。我们还为任何图类和任意范围提供了一种过滤方案。