We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular unions of self-avoiding walks) in the subgraph of the lattice graph generated from the support of the bi-adjacency matrix. The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.

翻译：我们研究确定性图构造，使得无论矩阵元素取值如何，低秩矩阵的独特完备化在一般情况下均可能实现。我们将完备性与格图子图中特定模式（自回避行走的特殊并集）的存在性相关联，该子图由双邻接矩阵支撑集生成。该构造使得设计无限族图成为可能，在这些图上，通过平方和层级方法，每个固定秩矩阵均可实现精确且稳定的完备化。