### Abstract

In this paper we study the 0-1 inverse maximum stable set problem, denoted by I S_{{0, 1}}. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider I S_{{0, 1}} against a specific algorithm such as G r e e d y and 2 o p t, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by I S_{{0, 1}, g r e e d y} and I S_{{0, 1}, 2 o p t}, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of 2 - Θ (frac(1, sqrt(l o g Δ))) for I S_{{0, 1}, 2 o p t}. Thirdly, we study the tractability of I S_{{0, 1}} for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of I S_{{0, 1}} and I S_{{0, 1}, 2 o p t} for some other classes of graphs.

Original language | English |
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Pages (from-to) | 2501-2516 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2008 Jul 6 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*156*(13), 2501-2516. https://doi.org/10.1016/j.dam.2008.03.015

}

*Discrete Applied Mathematics*, vol. 156, no. 13, pp. 2501-2516. https://doi.org/10.1016/j.dam.2008.03.015

**The 0-1 inverse maximum stable set problem.** / Chung, Yerim; Demange, Marc.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The 0-1 inverse maximum stable set problem

AU - Chung, Yerim

AU - Demange, Marc

PY - 2008/7/6

Y1 - 2008/7/6

N2 - In this paper we study the 0-1 inverse maximum stable set problem, denoted by I S{0, 1}. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider I S{0, 1} against a specific algorithm such as G r e e d y and 2 o p t, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by I S{0, 1}, g r e e d y and I S{0, 1}, 2 o p t, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of 2 - Θ (frac(1, sqrt(l o g Δ))) for I S{0, 1}, 2 o p t. Thirdly, we study the tractability of I S{0, 1} for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of I S{0, 1} and I S{0, 1}, 2 o p t for some other classes of graphs.

AB - In this paper we study the 0-1 inverse maximum stable set problem, denoted by I S{0, 1}. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider I S{0, 1} against a specific algorithm such as G r e e d y and 2 o p t, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by I S{0, 1}, g r e e d y and I S{0, 1}, 2 o p t, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of 2 - Θ (frac(1, sqrt(l o g Δ))) for I S{0, 1}, 2 o p t. Thirdly, we study the tractability of I S{0, 1} for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of I S{0, 1} and I S{0, 1}, 2 o p t for some other classes of graphs.

UR - http://www.scopus.com/inward/record.url?scp=49749125944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49749125944&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2008.03.015

DO - 10.1016/j.dam.2008.03.015

M3 - Article

VL - 156

SP - 2501

EP - 2516

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 13

ER -