### Abstract

Given a graph G on n nodes the authors say that a graph T on n + k nodes is a k-fault tolerant version of G, if one can embed G in any n node induced subgraph of T. Thus T can sustain k faults and still emulate G without any performance degradation. They show that for a wide range of values of n, k and d, for any graph on n nodes with maximum degree d there is a k-fault tolerant graph with maximum degree O(kd). They provide lower bounds as well: there are graphs G with maximum degree d such that any k-fault tolerant version of them has maximum degree at least Omega (d square root k).

Original language | English (US) |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 693-702 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: Oct 24 1992 → Oct 27 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country | United States |

City | Pittsburgh |

Period | 10/24/92 → 10/27/92 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

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## Cite this

Ajtai, M., Alon, N., Bruck, J., Cypher, R., Ho, C. T., Naor, M., & Szémeredi, E. (1992). Fault tolerant graphs, perfect hash functions and disjoint paths. In

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992*(pp. 693-702). [267781] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October). IEEE Computer Society. https://doi.org/10.1109/SFCS.1992.267781