### Abstract

In this paper we show that an optimal vertex ranking of a permutation graph can be computed in time O(n^{6}), where n is the number of vertices. The demonstrated minimal separator approach can also be used for designing polynomial time algorithms computing an optimal vertex ranking on the following classes of well-structured graphs: circular permutation graphs, interval graphs, circular arc graphs, trapezoid graphs and cocomparability graphs of bounded dimension.

Original language | English (US) |
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Title of host publication | STACS 1994 - 11th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings |

Editors | Ernst W. Mayr, Klaus W. Wagner, Patrice Enjalbert |

Publisher | Springer Verlag |

Pages | 747-758 |

Number of pages | 12 |

ISBN (Print) | 9783540577850 |

State | Published - Jan 1 1994 |

Event | Proceedings of the 11th Symposium on Theoretical Aspects of Computer Science (STACS'94) - Caen, Fr Duration: Feb 24 1994 → Feb 26 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 775 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Proceedings of the 11th Symposium on Theoretical Aspects of Computer Science (STACS'94) |
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City | Caen, Fr |

Period | 2/24/94 → 2/26/94 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*STACS 1994 - 11th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings*(pp. 747-758). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 775 LNCS). Springer Verlag.

**On vertex ranking for permutation and other graphs.** / Deogun, J. S.; Kloks, T.; Kratsch, D.; Müller, H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*STACS 1994 - 11th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 775 LNCS, Springer Verlag, pp. 747-758, Proceedings of the 11th Symposium on Theoretical Aspects of Computer Science (STACS'94), Caen, Fr, 2/24/94.

}

TY - GEN

T1 - On vertex ranking for permutation and other graphs

AU - Deogun, J. S.

AU - Kloks, T.

AU - Kratsch, D.

AU - Müller, H.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - In this paper we show that an optimal vertex ranking of a permutation graph can be computed in time O(n6), where n is the number of vertices. The demonstrated minimal separator approach can also be used for designing polynomial time algorithms computing an optimal vertex ranking on the following classes of well-structured graphs: circular permutation graphs, interval graphs, circular arc graphs, trapezoid graphs and cocomparability graphs of bounded dimension.

AB - In this paper we show that an optimal vertex ranking of a permutation graph can be computed in time O(n6), where n is the number of vertices. The demonstrated minimal separator approach can also be used for designing polynomial time algorithms computing an optimal vertex ranking on the following classes of well-structured graphs: circular permutation graphs, interval graphs, circular arc graphs, trapezoid graphs and cocomparability graphs of bounded dimension.

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UR - http://www.scopus.com/inward/citedby.url?scp=0008491536&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0008491536

SN - 9783540577850

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 747

EP - 758

BT - STACS 1994 - 11th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

A2 - Mayr, Ernst W.

A2 - Wagner, Klaus W.

A2 - Enjalbert, Patrice

PB - Springer Verlag

ER -