Hereditary Properties of Ordered Graphs

An ordered graph is a graph together with a linear order on its vertices. A hereditary property of ordered graphs is a collection of ordered graphs closed under taking order-preserving isomorphisms of the vertex set, and order-preserving induced subgraphs. If P is a hereditary property of ordered graphs, then P n denotes the collection \( \left\{ {G \in \mathcal{P}:V(G) = [n]} \right\} \), and the function \( n \mapsto \left| {\mathcal{P}_n } \right| \) is called the speed of P.

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