We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite the many results and the extensive research effort, there is no characterization of the properties that are strongly testable (i.e. testable with constant query complexity) even for 1-sided error tests. The bounded-degree model can naturally be generalized to directed graphs resulting in two models that were considered in the literature. The first contains the directed graphs in which the out-degree is bounded but the in-degree is not restricted. In the other, both the out-degree and in-degree are bounded. We give a characterization of the 1-sided error strongly testable monotone graph properties and the 1-sided error strongly testable hereditary graph properties in all the bounded-degree directed and undirected graphs models.

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关于有界度图的单边误差强可测图性质的表征

我们研究了有界度图模型中（双）图属性的属性测试。有界度模型中图性质的研究是近 15 年来性质测试研究的重点方向之一。然而，尽管有许多结果和广泛的研究工作，但即使对于单边错误测试，也没有强可测试性（即可测试具有恒定查询复杂性）的特性的表征。有界度模型可以自然地推广到有向图，从而产生文献中考虑的两种模型。第一个包含出度有界但入度不受限制的有向图。另一方面，出度和入度都是有界的。