## Abstract

Given a class of structures with a notion of connectedness (satisfying some reasonable assumptions), we consider the limit (as n → ∞) of the probability that a random (labelled or unlabelled) n-element structure in the class is connected. The paper consists of three parts: two specific examples, N-free graphs and posets, where the limiting probability of connectedness is one-half and the golden ratio respectively; an investigation of the relation between this question and the growth rate of the number of structures in the class; and a generalisation of the problem to other combinatorial constructions motivated in part by the group-theoretic constructions of direct and wreath product.

Original language | English |
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Pages (from-to) | 175-187 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 167-168 |

DOIs | |

Publication status | Published - 15 Apr 1997 |