### Abstract

The edge deletion problem (EDP) corresponding to a given class H of graphs is to find the minimum number of edges the deletion of which from a given graph G results in a subgraph G', G' epsilon H. Previous complexity results are extended by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard. (1) H is defined by a set of forbidden homeomorphs or minors in which every member is a 2-connected graph with minimum degree three; (2) BH is defined by K//4 - e as a forbidden homeomorph or minor; and (3) H is defined by P//l, l greater than equivalent to 3, the simple path on l nodes, as a forbidden induced subgraph.

Original language | English (US) |
---|---|

Pages (from-to) | 354-362 |

Number of pages | 9 |

Journal | IEEE Transactions on Circuits and Systems |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1988 |

Externally published | Yes |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*IEEE Transactions on Circuits and Systems*,

*35*(3), 354-362. https://doi.org/10.1109/31.1748

**COMPLEXITY OF SOME EDGE DELETION PROBLEMS.** / El-Mallah, Ehab S.; Colbourn, Charles.

Research output: Contribution to journal › Article

*IEEE Transactions on Circuits and Systems*, vol. 35, no. 3, pp. 354-362. https://doi.org/10.1109/31.1748

}

TY - JOUR

T1 - COMPLEXITY OF SOME EDGE DELETION PROBLEMS.

AU - El-Mallah, Ehab S.

AU - Colbourn, Charles

PY - 1988/3

Y1 - 1988/3

N2 - The edge deletion problem (EDP) corresponding to a given class H of graphs is to find the minimum number of edges the deletion of which from a given graph G results in a subgraph G', G' epsilon H. Previous complexity results are extended by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard. (1) H is defined by a set of forbidden homeomorphs or minors in which every member is a 2-connected graph with minimum degree three; (2) BH is defined by K//4 - e as a forbidden homeomorph or minor; and (3) H is defined by P//l, l greater than equivalent to 3, the simple path on l nodes, as a forbidden induced subgraph.

AB - The edge deletion problem (EDP) corresponding to a given class H of graphs is to find the minimum number of edges the deletion of which from a given graph G results in a subgraph G', G' epsilon H. Previous complexity results are extended by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard. (1) H is defined by a set of forbidden homeomorphs or minors in which every member is a 2-connected graph with minimum degree three; (2) BH is defined by K//4 - e as a forbidden homeomorph or minor; and (3) H is defined by P//l, l greater than equivalent to 3, the simple path on l nodes, as a forbidden induced subgraph.

UR - http://www.scopus.com/inward/record.url?scp=0023981241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023981241&partnerID=8YFLogxK

U2 - 10.1109/31.1748

DO - 10.1109/31.1748

M3 - Article

AN - SCOPUS:0023981241

VL - 35

SP - 354

EP - 362

JO - IEEE Transactions on Circuits and Systems

JF - IEEE Transactions on Circuits and Systems

SN - 0098-4094

IS - 3

ER -