Filtering Hyperedge-Replacement Through Compatible Properties

In this paper, we demonstrate that the set of all hypergraphs of a hyperedge-replacement language that satisfy a so-called compatible property can again be generated by a hyperedge-replacement grammar. Because many familiar graph-theoretic properties like connectedness, k-colorability, planarity, the existence of Eulerian and Hamiltonian paths and cycles, etc. are compatible and compatibility is closed under Boolean operations, the members of a hyperedge-replacement language can be filtered through the sieve of various desirable and undesirable properties easily on the syntactic level of the generative grammar rules.