A Note on Graph Decimation

To avoid paradoxes in parallel graph rewriting, it is desirable to forbid overlapping instances of a subgraph to be rewritten simultaneously. The selection of maximal sets of nonoverlapping instances corresponds to the selection of maximal independent sets of nodes in a derived graph. This note briefly examines the process of repeatedly selecting such sets of nodes. It shows that doing so “decimates” the graph in the sense that the number of nodes shrinks exponentially; but that unfortunately, the degree of the graph may grow exponentially.