### Abstract

A graph G = (V, E) is called a generic circuit if E = 2 V - 2 and every X ⊂ V with 2≤ X ≤ V - 1 satisfies i(X)≤2 X - 3. Here i(X) denotes the number of edges induced by X. The operation extension subdivides an edge uw of a graph by a new vertex v and adds a new edge vz for some vertex z ≠ u, w. Connelly conjectured that every 3-connected generic circuit can be obtained from K_{4} by a sequence of extensions. We prove this conjecture. As a corollary, we also obtain a special case of a conjecture of Hendrickson on generically globally rigid graphs.

Original language | English |
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Pages (from-to) | 77-97 |

Number of pages | 21 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 88 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 1 2003 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics