## Abstract

A digraph D is homogeneously embedded in a digraph H if for each vertex x of D and each vertex y of H, there exists an embedding of D in H as an induced subdigraph with x at y. A digraph F of minimum order in which D can be homogeneously embedded is called a frame of D and the order of F is called the framing number of D. Several general results involving frames and framing numbers of digraphs are established. The framing number is determined for a number of classes of digraphs, including a class of digraphs whose underlying graph is a complete bipartite graph, a class of digraphs whose underlying graph is C_{n} + K_{1}, and the lexicographic product of a transitive tournament and a vertex transitive digraph. A relationship between the diameters of the underlying graphs of a digraph and its frame is determined. We show that every tournament has a frame which is also a tournament.

Original language | English |
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Pages (from-to) | 115-133 |

Number of pages | 19 |

Journal | Discrete Applied Mathematics |

Volume | 82 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2 Mar 1998 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics