Abstract
Graph-rewriting has been a growing discipline for over three decades. It grew out of the study of graph grammars, in which – analogously to string and tree grammars – a principal interest was to describe the families of graphs that could be generated from a given set of productions. A fundamental contribution was, of course, the double-pushout construction of Ehrig and his colleagues [4]; it made precise how the left-hand side of a production, or rewriting rule, could be found to occur in a host graph, and how it should then be replaced by the right-hand side. This break-through led to many theoretical developments and many applications. It relies firmly upon the treatment of graphs as objects in a category whose arrows are embedding maps.
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Milner, R. (2005). Embeddings and Contexts for Link Graphs. In: Kreowski, HJ., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds) Formal Methods in Software and Systems Modeling. Lecture Notes in Computer Science, vol 3393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31847-7_20
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