## Abstract

This paper begins with the observation that half of all graphs containing no induced path of length 3 are disconnected. We generalize this in several directions. First, we give necessary and sufficient conditions (in terms of generating functions) for the probability of connectedness in a suitable class of graphs to tend to a limit strictly between zero and one. Next we give a general framework in which this and related questions can be posed, involving operations on classes of finite structures. Finally, we discuss briefly an algebra associated with such a class of structures, and give a conjecture about its structure.

Original language | English |
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Pages (from-to) | 31-43 |

Number of pages | 13 |

Journal | Combinatorics Probability and Computing |

Volume | 8 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Jan 1999 |