### Abstract

Let G = (V,A) be a directed graph. With any subset X of V is associated the directed subgraph G[X] = (X,A ∩ (X × X)) of G induced by X. A subset X of V is an interval of G provided that for a, b ∈ X and x ∈ V \ X, (a, x) ∈ A if and only if (b, x) ∈ A, and similarly for (x, a) and (x, b). For example ∅, V, and {x}, where x ∈ V , are intervals of G which are the trivial intervals. A directed graph is indecomposable if all its intervals are trivial. Given an integer k > 0, a directed graph G = (V,A) is called an indecomposable k- covering provided that for every subset X of V with |X| ≤ k, there exists a subset Y of V such that X ⊆ Y , G[Y] is indecomposable with |Y| ≥ 3. In this paper, the indecomposable k-covering directed graphs are characterized for any k > 0.

Original language | English (US) |
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Pages (from-to) | 37-44 |

Number of pages | 8 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 31 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 |

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### Keywords

- decomposition tree
- indecomposable
- interval
- k-covering

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discussiones Mathematicae - Graph Theory*,

*31*(1), 37-44. https://doi.org/10.7151/dmgt.1528