### Abstract

A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. We present a polynomial-time algorithm to find a c-vertex-ranking of a partial k-tree using the minimum number of ranks for any bounded integers c and k.

Original language | English |
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Title of host publication | Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings |

Editors | Tao Jiang, D.T. Lee |

Publisher | Springer-Verlag |

Pages | 212-221 |

Number of pages | 10 |

ISBN (Print) | 354063357X, 9783540633570 |

Publication status | Published - 1997 Jan 1 |

Event | 3rd Annual International Computing and Combinatorics Conference, COCOON 1997 - Shanghai, China Duration: 1997 Aug 20 → 1997 Aug 22 |

### 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 | 1276 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Annual International Computing and Combinatorics Conference, COCOON 1997 |
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Country | China |

City | Shanghai |

Period | 97/8/20 → 97/8/22 |

### Keywords

- Algorithm
- Partial k-tree
- Separator tree
- Treewidth
- Vertexranking

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Kashem, M. A., Zhou, X., & Nishizeki, T. (1997). Generalized vertex-rankings of partial k-trees. In T. Jiang, & D. T. Lee (Eds.),

*Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings*(pp. 212-221). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1276). Springer-Verlag.