Hereditary properties of ordered graphs
摘要
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 induced ordered subgraphs. If P is a property of ordered graphs, then the function which counts the number of ordered graphs in P with exactly n vertices is called the speed of P. In this paper we determine the possible speeds of a hereditary property of ordered graphs, up to the speed 2^(n-1). In particular, we prove that there exists a jump from polynomial speed to speed F(n), the Fibonacci numbers, and that there exists an infinite sequence of subsequent jumps, from p(n)F(n,k) to F(n,k+1) (where p(n) is a polynomial and F(n,k) are the generalized Fibonacci numbers) converging to 2^(n-1). Our results generalize a theorem of Kaiser and Klazar, who proved that the same jumps occur for hereditary properties of permutations.
引用
@article{arxiv.math/0702352,
title = {Hereditary properties of ordered graphs},
author = {József Balogh and Béla Bollobás and Robert Morris},
journal= {arXiv preprint arXiv:math/0702352},
year = {2007}
}
备注
39 pgs, 1 figure