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.

翻译：图形域变量和限制是Dooms 等人推出的制约性编程的延伸。 Fages在其博士论文中对此方法进行了进一步调查。 另一方面, Beldiceanu 等人提出了基于图形属性的全球制约性通用过滤方案。这个方案非常依赖图形属性界限的计算,并可在图形域变量和限制的背景下使用,但需作一些调整。MIN_NCC和MAX_NCC的界碑已被确定为基于图形的路径路径_ with_loops 图形类的全球制约性表示。我们在此注释中,我们对这些图形域变量和任何图形类的界限进行了概括化。我们还为任何图形类别和任意界限提供了一个过滤方案。