### Abstract

Given a tournament score sequences_{1}≥s_{2}≥...≥s_{n}, we prove that there exists a tournamentTon vertex set (1, 2, ..., n) such that the degree of any vertexiiss_{i}and the subtournaments ofTon both the even and the odd vertices are transitive in the given order. This means thatibeatsjwheneveri2/2 reversals are always enough and that in some cases (1-o(1))n^{2}/32 are required. We also show that such a sequence of triangle reversals can be found inO(n^{2}) time.

Original language | English |
---|---|

Pages (from-to) | 181-196 |

Number of pages | 16 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 72 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1998 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*72*(2), 181-196. https://doi.org/10.1006/jctb.1997.1806

**2-Partition-Transitive Tournaments.** / Guiduli, Barry; Gyárfás, A.; Thomassé, Stéphan; Weidl, Peter.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 72, no. 2, pp. 181-196. https://doi.org/10.1006/jctb.1997.1806

}

TY - JOUR

T1 - 2-Partition-Transitive Tournaments

AU - Guiduli, Barry

AU - Gyárfás, A.

AU - Thomassé, Stéphan

AU - Weidl, Peter

PY - 1998/3

Y1 - 1998/3

N2 - Given a tournament score sequences1≥s2≥...≥sn, we prove that there exists a tournamentTon vertex set (1, 2, ..., n) such that the degree of any vertexiissiand the subtournaments ofTon both the even and the odd vertices are transitive in the given order. This means thatibeatsjwheneveri2/2 reversals are always enough and that in some cases (1-o(1))n2/32 are required. We also show that such a sequence of triangle reversals can be found inO(n2) time.

AB - Given a tournament score sequences1≥s2≥...≥sn, we prove that there exists a tournamentTon vertex set (1, 2, ..., n) such that the degree of any vertexiissiand the subtournaments ofTon both the even and the odd vertices are transitive in the given order. This means thatibeatsjwheneveri2/2 reversals are always enough and that in some cases (1-o(1))n2/32 are required. We also show that such a sequence of triangle reversals can be found inO(n2) time.

UR - http://www.scopus.com/inward/record.url?scp=0039657369&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039657369&partnerID=8YFLogxK

U2 - 10.1006/jctb.1997.1806

DO - 10.1006/jctb.1997.1806

M3 - Article

AN - SCOPUS:0039657369

VL - 72

SP - 181

EP - 196

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 2

ER -