## Abstract

A graph G = (V, E) is chordal probe if its vertices can be partitioned into two sets P (probes) and N (non-probes) where N is a stable set and such that G can be extended to a chordal graph by adding edges between non-probes. The study of chordal probe graphs was originally motivated as a generalization of the interval probe graphs which occur in applications involving physical mapping of DNA. However, chordal probe graphs also have their own computational biology application as a special case of constructing phytogenies, tree structures which model genetic mutations. We give several characterizations of chordal probe graphs, first in the case of a fixed given partition of the vertices into probes and non-probes, and second in the more general case where no partition is given. In both of these cases, our results are obtained by characterizing superclasses, namely, N-triangulatable graphs and cycle-bicolorable graphs, which are first introduced here. We give polynomial time recognition algorithms for each class. The complexity is O(|P||E|), given a partition of the vertices into probes and non-probes, thus also providing a interesting tractible subcase of the chordal graph sandwich problem. If no partition is given in advance, the complexity of our recognition algorithm is O(|V|^{2}|E|).

Original language | English |
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Pages | 955-962 |

Number of pages | 8 |

State | Published - 2004 |

Event | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States Duration: 11 Jan 2004 → 13 Jan 2004 |

### Conference

Conference | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country/Territory | United States |

City | New Orleans, LA. |

Period | 11/01/04 → 13/01/04 |

## ASJC Scopus subject areas

- Software
- General Mathematics