### Abstract

If the paths of length ≤s, joining two non-adjacent vertices u, υ of a graph cannot be destroyed by deleting less than t vertices, then there are at least t internally vertex-disjoint paths joining u and υ, each having length less than ( t+s-2 s-2)+( t+s-3 s-2). Some constructions show that using paths of length at least s t-1^{t} might be necessary.

Original language | English |
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Pages (from-to) | 161-174 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 120 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Sep 12 1993 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*120*(1-3), 161-174. https://doi.org/10.1016/0012-365X(93)90573-C

**Menger-type theorems with restrictions on path lengths.** / Pyber, László; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 120, no. 1-3, pp. 161-174. https://doi.org/10.1016/0012-365X(93)90573-C

}

TY - JOUR

T1 - Menger-type theorems with restrictions on path lengths

AU - Pyber, László

AU - Tuza, Z.

PY - 1993/9/12

Y1 - 1993/9/12

N2 - If the paths of length ≤s, joining two non-adjacent vertices u, υ of a graph cannot be destroyed by deleting less than t vertices, then there are at least t internally vertex-disjoint paths joining u and υ, each having length less than ( t+s-2 s-2)+( t+s-3 s-2). Some constructions show that using paths of length at least s t-1t might be necessary.

AB - If the paths of length ≤s, joining two non-adjacent vertices u, υ of a graph cannot be destroyed by deleting less than t vertices, then there are at least t internally vertex-disjoint paths joining u and υ, each having length less than ( t+s-2 s-2)+( t+s-3 s-2). Some constructions show that using paths of length at least s t-1t might be necessary.

UR - http://www.scopus.com/inward/record.url?scp=43949172049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949172049&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(93)90573-C

DO - 10.1016/0012-365X(93)90573-C

M3 - Article

VL - 120

SP - 161

EP - 174

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -