We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize several theorems from the literature and yield further algebraic invariance properties that must be satisfied in every such graph. Algebraic properties of this kind are tightly connected to the tractability of constraint satisfaction problems, and we obtain new such properties even for infinite countably categorical graphs. We balance these positive results by showing the existence of a countably categorical hypergraph that fails to interpret some finite structure, while still lacking some of the most essential algebraic invariance properties known to hold for finite structures.

翻译：本文研究在给定有向图无法通过原始正解释（带参数或轨道）解释每个有限结构的条件下，所引发的结构性质。我们的结果推广了文献中的若干定理，并推导出此类图必须满足的进一步代数不变性质。这类代数性质与约束满足问题的易解性密切相关，即便对于无限可数范畴图，我们也获得了此类新性质。为平衡这些正面结果，我们证明存在一个可数范畴超图，该图虽无法解释某些有限结构，但仍缺乏已知对有限结构成立的最本质代数不变性质中的若干项。