Propagation Tree Decompositions and Linearly Independent Vertices
e 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.
Mitchell, L. (2020). Propagation tree decompositions and linearly independent vertices. Theoretical Computer Science. https://doi.org/10.1016/j.tcs.2020.10.016.