One of the most basic facts related to the famous Ulam reconstruction conjecture is that the connectedness of a graph can be determined by the deck of its vertex-deleted subgraphs, which are considered up to isomorphism. We strengthen this result by proving that connectedness can still be determined when the subgraphs in the deck are given up to equivalence under the color refinement isomorphism test. Consequently, this implies that connectedness is recognizable by Reconstruction Graph Neural Networks, a recently introduced GNN architecture inspired by the reconstruction conjecture (Cotta, Morris, Ribeiro 2021).

翻译：关于著名的乌拉姆重构猜想，一个最基本的事实是：图是否连通可以通过其顶点删除子图的牌组（在同构意义下）来确定。我们通过证明即使牌组中的子图仅在颜色细化同构测试的等价意义下给出，连通性仍可被判定，从而强化了这一结果。这进而意味着连通性可被重构图神经网络（Reconstruction Graph Neural Networks）所识别，这是一种近期受重构猜想启发而提出的图神经网络架构（Cotta, Morris, Ribeiro 2021）。