### Abstract

A subset S of k vertices in a k-connected graph G is a shredder, if G - S has at least three components. We show that if G has n vertices, then the number of shredders is at most n, which was conjectured by Cheriyan and Thurimella [Cheriyan & Thurimella, Proc 28th Ann ACM Symp, 1996]. If G contains no meshing shredders (in particular, if k ≤ 3), the sharp upper bound [(n - k - 1)/2] is proven.

Original language | English |
---|---|

Pages (from-to) | 195-200 |

Number of pages | 6 |

Journal | Journal of Graph Theory |

Volume | 31 |

Issue number | 3 |

Publication status | Published - Jul 1999 |

### Fingerprint

### Keywords

- Connectivity
- k-connected graphs
- Minimum cuts

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the number of shredders.** / Jordán, T.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the number of shredders

AU - Jordán, T.

PY - 1999/7

Y1 - 1999/7

N2 - A subset S of k vertices in a k-connected graph G is a shredder, if G - S has at least three components. We show that if G has n vertices, then the number of shredders is at most n, which was conjectured by Cheriyan and Thurimella [Cheriyan & Thurimella, Proc 28th Ann ACM Symp, 1996]. If G contains no meshing shredders (in particular, if k ≤ 3), the sharp upper bound [(n - k - 1)/2] is proven.

AB - A subset S of k vertices in a k-connected graph G is a shredder, if G - S has at least three components. We show that if G has n vertices, then the number of shredders is at most n, which was conjectured by Cheriyan and Thurimella [Cheriyan & Thurimella, Proc 28th Ann ACM Symp, 1996]. If G contains no meshing shredders (in particular, if k ≤ 3), the sharp upper bound [(n - k - 1)/2] is proven.

KW - Connectivity

KW - k-connected graphs

KW - Minimum cuts

UR - http://www.scopus.com/inward/record.url?scp=0033468580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033468580&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033468580

VL - 31

SP - 195

EP - 200

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -