We explore the relationship between propagation tree decompositions of a graph of a given size and the OS-sets of the same size, showing that each can generate the other. We give a short constructive proof that the OS-sets are in bijective correspondence with a subset of the propagation tree decompositions.

中文翻译：

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传播树分解和线性独立顶点

我们探索了给定大小的图的传播树分解与相同大小的OS集之间的关系，显示了每个可以生成另一个。我们给出了一个简短的建设性证明，即OS集与传播树分解的子集是双射的对应。