The n‐ordered graphs: A new graph class

Abstract

Abstract. For a positive integer n, we introduce the new graph class of n-ordered graphs, which generalize partial n-trees. Several characterizations are given for the finite n-ordered graphs, including one via a combinatorial game.We introduce new countably infinite graphs R (n) , which we name the infinite random n-ordered graphs. The graphs R (n) play a crucial role in the theory of n-ordered graphs, and are inspired by recent research on the web graph and the infinite random graph. We characterize R (n) as a limit of a random process, and via an adjacency property and a certain folding operation. We prove that the induced subgraphs of R (n) are exactly the countable n-ordered graphs. We show that all countable groups embed in the automorphism group of R (n) .