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Graph Structure and Monadic Second-Order Logic by Joost Engelfriet, Bruno Courcelle

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1.9 Relational structures

Terms, graphs, labeled graphs, hypergraphs of different types are, or rather can be conveniently represented by relational structures. Up to now, we have only seen relational structures with unary and binary relations that correspond to vertex- and edge-labeled graphs. However, many of our results can be proved without any difficulty for general relational structures.

In order to illustrate the usefulness of relational structures in Discrete Mathematics, we will present the examples of betweenness relations and cyclic orderings, two combinatorial notions defined in a natural way as ternary relations. Furthermore, in a different domain, the theory of relational databases is based on the concept of relational structure ...

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