Properties of graphs preserved by relational graph rewritings

Abstract

We formulate graphs and graph rewritings using binary relations and call them relational graphs and relational graph rewritings. In this framework, rewriting is defined using a pushout in a category of relational graphs. It is known that an important theorem of rewriting systems called critical pair's lemma can be proved using simple and clear categorical properties. In this paper, we construct treelike graphs and Raoult Graphs by some relational conditions. We give a sufficient condition for rewriting rules and matchings which guarantees the closedness of those graph rewritings. These results show that the critical pair's lemma also holds under some conditions for a graph rewriting system in which graphs are restricted to treelike graphs or Raoult Graphs.