### Abstract

An edge of a 3-connected graph is called contractible if its contraction results in a 3-connected graph. Ando, Enomoto and Saito proved that every 3-connected graph of order at least five has ⌈|G|/2⌉ or more contractible edges. As another lower bound, we prove that every 3-connected graph, except for six graphs, has at least (2|E(G)| + 12)/7 contractible edges. We also determine the extremal graphs. Almost all of these extremal graphs G have more than ⌈|G|/2⌉ contractible edges.

Original language | English |
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Pages (from-to) | 333-354 |

Number of pages | 22 |

Journal | Graphs and Combinatorics |

Volume | 4 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1988 Dec 1 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics