We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set of connected triples, making unique reconstruction of the original graph from the triples impossible. We identify some families of graphs (including triangle-free graphs) for which all graphs have a different set of connected triples. We also give algorithms that reconstruct a graph from a set of triples, and for testing if this reconstruction is unique. Finally, we study a possible extension of the model in which the subsets of size $k$ that induce a connected graph are given for larger (fixed) values of $k$.

翻译：我们在图表中引入了一种不确定性的新模型:输入没有指定图形的所有边缘,而是包含构成连接子图的所有三重脊椎。 一般来说, 不同的( 标签的) 图表可能有一套相同的连接三重, 使得从三重图中重建原始图形成为不可能的。 我们确定一些图表的组合( 包括无三角图), 所有图表都有一套不同的连接三重图 。 我们还给出算法, 从一组三重图中重建一个图表, 并测试这一重建是否独特 。 最后, 我们研究一个可能的模型的扩展, 在其中为较大( 固定的) $K 值给出一个链接图的子集。</s>