Hereditary Properties of Ordered Graphs

  title={Hereditary Properties of Ordered Graphs},
  author={B{\'e}la Bollob{\'a}s and Robert Morris},
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 Pn denotes the collection {G ∈ P : V (G) = [n]}, and the function n 7→ |Pn| is called the speed of P . The possible speeds of a hereditary property of labelled graphs have been extensively… CONTINUE READING