Automatic Deduction of Induced Subgraphs of Some Infinite Families of Graphs

Graph class C is induced-hereditary if for every graph G in C, every induced subgraph of G belongs to C. Induced-hereditary graph classes allow characterisation by sets of forbidden induced subgraphs. Such characterisations are very useful for automatic deduction of relations between graph classes. However, sometimes those sets of forbidden induced subgraphs are infinite, what makes it difficult to work with them. We introduce Head-Mid-Tail grammars (a partial case of hyperedge replacement grammars, [1]) which have the property that if an infinite family F can be defined by a Head-Mid-Tail grammar G, then it is decidable whether a finite set S of graphs forbids the (infinite) family F, given by G.