## A Linear Time Algorithm to Compute a Dominating Path in an AT-free Graph (1998)

Venue: | Inform. Process. Lett |

Citations: | 12 - 3 self |

### BibTeX

@ARTICLE{Corneil98alinear,

author = {Derek G. Corneil and Stephan Olariu and Lorna Stewart},

title = {A Linear Time Algorithm to Compute a Dominating Path in an AT-free Graph},

journal = {Inform. Process. Lett},

year = {1998},

volume = {54},

pages = {253--257}

}

### Years of Citing Articles

### OpenURL

### Abstract

An independent set fx; y; zg is called an asteroidal triple if between any pair in the triple there exists a path that avoids the neighborhood of the third. A graph is referred to as AT-free if it does not contain an asteroidal triple. We present a simple linear-time algorithm to compute a dominating path in a connected AT-free graph. Keywords. asteroidal triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs [10], permutation graphs [6], trapezoid graphs [3, 5], and cocomparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of graphs [2, 5, 7, 8, 9, 11, 12]. As it turns out, the classes mentioned above are all subfamilies of a class of graphs called the asteroidal triple-free graphs (AT-free graphs, for short). An independent triple fx; y; zg is called an asteroidal triple if between any p...

### Citations

1207 |
Algorithmic Graph Theory and Perfect Graphs
- Golumbic
- 1980
(Show Context)
Citation Context ...comparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of graphs =-=[2, 5, 7, 8, 9, 11, 12]-=-. As it turns out, the classes mentioned above are all subfamilies of a class of graphs called the asteroidal triple-free graphs (AT-free graphs, for short). An independent triple fx; y; zg is called ... |

141 |
Representation of a finite graph by a set of intervals on the real line
- Lekkerkerker, Boland
- 1962
(Show Context)
Citation Context ...ithm to compute a dominating path in a connected AT-free graph. Keywords. asteroidal triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs =-=[10]-=-, permutation graphs [6], trapezoid graphs [3, 5], and cocomparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a se... |

41 |
Graph Theory and its Applications to Problems of Society
- Roberts
- 1978
(Show Context)
Citation Context ...comparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of graphs =-=[2, 5, 7, 8, 9, 11, 12]-=-. As it turns out, the classes mentioned above are all subfamilies of a class of graphs called the asteroidal triple-free graphs (AT-free graphs, for short). An independent triple fx; y; zg is called ... |

29 |
Domination on cocomparability graphs
- Kratsch, Stewart
- 1993
(Show Context)
Citation Context ...comparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of graphs =-=[2, 5, 7, 8, 9, 11, 12]-=-. As it turns out, the classes mentioned above are all subfamilies of a class of graphs called the asteroidal triple-free graphs (AT-free graphs, for short). An independent triple fx; y; zg is called ... |

29 |
An optimal greedy heuristic to color interval graphs
- Olariu
- 1991
(Show Context)
Citation Context |

28 |
Trapezoid graphs and their coloring
- Dagan, Golumbic, et al.
- 1988
(Show Context)
Citation Context ...d AT-free graph. Keywords. asteroidal triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs [10], permutation graphs [6], trapezoid graphs =-=[3, 5]-=-, and cocomparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of... |

28 |
Permutation graphs and transitive graphs
- Even, Pnueli, et al.
- 1972
(Show Context)
Citation Context ...ing path in a connected AT-free graph. Keywords. asteroidal triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs [10], permutation graphs =-=[6]-=-, trapezoid graphs [3, 5], and cocomparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algor... |

17 |
Extensions of permutation and interval graphs
- Corneil, Kamula
- 1987
(Show Context)
Citation Context ...d AT-free graph. Keywords. asteroidal triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs [10], permutation graphs [6], trapezoid graphs =-=[3, 5]-=-, and cocomparability graphs [8] feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of... |

4 |
Rangan, Connected domination and Steiner set on asteroidal triple-free graphs
- Balakrishnan, Rajaraman, et al.
- 1993
(Show Context)
Citation Context ...nected AT-free graph is a dominating pair if every x; y-path is dominating. In [4] it has been shown that every connected AT-free graph contains a dominating pair. Quite recently, Balakrishnan et al. =-=[1]-=- have exhibited a straightforward algorithm that finds all dominating pairs in an arbitrary n-vertex graph in O(n 3 ) time. In particular, their algorithm can be used to find a dominating pair in a co... |

4 |
Monma and W.T
- Golumbic, L
- 1984
(Show Context)
Citation Context ...al triple-free graphs, domination, algorithms 1 Introduction A number of families of graphs including interval graphs [10], permutation graphs [6], trapezoid graphs [3, 5], and cocomparability graphs =-=[8]-=- feature a type of linear ordering of their vertex sets. It is precisely this linear ordering that is exploited in a search for efficient algorithms on these classes of graphs [2, 5, 7, 8, 9, 11, 12].... |

3 |
A recognition algorithm for II-graphs, Doctoral thesis
- Cheah
- 1990
(Show Context)
Citation Context |

2 |
The Yiddish catalog and authority file of the YIVO Library was edited by
- Corneil, Olariu, et al.
- 1998
(Show Context)
Citation Context ... graphs (AT-free graphs, for short). An independent triple fx; y; zg is called an asteroidal triple if between any pair in the triple there exists a path that avoids the neighborhood of the third. In =-=[4] it has be-=-en argued that the property of being asteroidal triple-free is what is enforcing the linear ordering of the vertex sets. One interesting "certificate" of linearity is the existence of a path... |