### Abstract

In this paper we investigate the following generalization of transitivity: A digraph D is (m,n)-transitive whenever there is a path of length m from x to y there is a subset of n+1 vertices of these m+1 vertices which contain a path of length n from x to y. Here we study various properties of (m,n)-transitive digraphs. In particular, (m,1)-transitive tournaments are characterized. Their similarities to transitive tournaments are analyzed and discussed. Various other results pertaining to (m,1)-transitive digraphs are given.

Original language | English |
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Pages (from-to) | 35-41 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 69 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1988 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*69*(1), 35-41. https://doi.org/10.1016/0012-365X(88)90175-6

**On a generalization of transitivity for digraphs.** / Gyárfás, A.; Jacobson, Michael S.; Kinch, Lael F.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 69, no. 1, pp. 35-41. https://doi.org/10.1016/0012-365X(88)90175-6

}

TY - JOUR

T1 - On a generalization of transitivity for digraphs

AU - Gyárfás, A.

AU - Jacobson, Michael S.

AU - Kinch, Lael F.

PY - 1988

Y1 - 1988

N2 - In this paper we investigate the following generalization of transitivity: A digraph D is (m,n)-transitive whenever there is a path of length m from x to y there is a subset of n+1 vertices of these m+1 vertices which contain a path of length n from x to y. Here we study various properties of (m,n)-transitive digraphs. In particular, (m,1)-transitive tournaments are characterized. Their similarities to transitive tournaments are analyzed and discussed. Various other results pertaining to (m,1)-transitive digraphs are given.

AB - In this paper we investigate the following generalization of transitivity: A digraph D is (m,n)-transitive whenever there is a path of length m from x to y there is a subset of n+1 vertices of these m+1 vertices which contain a path of length n from x to y. Here we study various properties of (m,n)-transitive digraphs. In particular, (m,1)-transitive tournaments are characterized. Their similarities to transitive tournaments are analyzed and discussed. Various other results pertaining to (m,1)-transitive digraphs are given.

UR - http://www.scopus.com/inward/record.url?scp=45449121842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45449121842&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(88)90175-6

DO - 10.1016/0012-365X(88)90175-6

M3 - Article

AN - SCOPUS:45449121842

VL - 69

SP - 35

EP - 41

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -