Abstract
A graph class is called A-free if every graph in the class has no graph in the set A as an induced subgraph. Such characterisations by forbidden induced subgraphs are (among other purposes) very useful for determining whether A-free is a subclass of B-free, by determining whether every graph in B has some graph in A as an induced subgraph. This requires solving the Subgraph Isomorphism Problem, which is NP-complete in general, but for which effective practical algorithms for general and specific purposes exist. However, if B is infinite, these algorithms cannot be used. We introduce Head-Mid-Tail grammars (a special case of hyperedge replacement grammars) which have the property that if an infinite set B can be defined by a Head-Mid-Tail grammar then it is decidable whether every graph in B contains some graph from a finite set A of graphs as an induced subgraph, thereby solving the A-free ⊆ B-free problem. Moreover, our algorithm is both simple and efficient enough to be practical.
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de Ridder, H.N., de Ridder, N. (2014). The Subgraph Isomorphism Problem on a Class of Hyperedge Replacement Languages. In: Giese, H., König, B. (eds) Graph Transformation. ICGT 2014. Lecture Notes in Computer Science, vol 8571. Springer, Cham. https://doi.org/10.1007/978-3-319-09108-2_13
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DOI: https://doi.org/10.1007/978-3-319-09108-2_13
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