# Large unavoidable subtournaments

Research output: Contribution to journal › Article › peer-review

## Standard

**Large unavoidable subtournaments.** / Long, Eoin.

Research output: Contribution to journal › Article › peer-review

## Harvard

*Combinatorics, Probability and Computing*, vol. 26, no. 1, pp. 68-77. https://doi.org/10.1017/S0963548316000213

## APA

*Combinatorics, Probability and Computing*,

*26*(1), 68-77. https://doi.org/10.1017/S0963548316000213

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## Author

## Bibtex

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## RIS

TY - JOUR

T1 - Large unavoidable subtournaments

AU - Long, Eoin

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let Dk denote the tournament on 3k vertices consisting of three disjoint vertex classes V1, V2 and V3 of size k, each oriented as a transitive subtournament, and with edges directed from V1 to V2, from V2 to V3 and from V3 to V1. Fox and Sudakov proved that given a natural number k and ε > 0, there is n0(k, ε) such that every tournament of order n ⩾ n0(k,ε) which is ε-far from being transitive contains Dk as a subtournament. Their proof showed that and they conjectured that this could be reduced to n0(k, ε) ⩽ ε−O(k). Here we prove this conjecture.

AB - Let Dk denote the tournament on 3k vertices consisting of three disjoint vertex classes V1, V2 and V3 of size k, each oriented as a transitive subtournament, and with edges directed from V1 to V2, from V2 to V3 and from V3 to V1. Fox and Sudakov proved that given a natural number k and ε > 0, there is n0(k, ε) such that every tournament of order n ⩾ n0(k,ε) which is ε-far from being transitive contains Dk as a subtournament. Their proof showed that and they conjectured that this could be reduced to n0(k, ε) ⩽ ε−O(k). Here we prove this conjecture.

KW - Tournaments

KW - Ramsey theory

U2 - 10.1017/S0963548316000213

DO - 10.1017/S0963548316000213

M3 - Article

VL - 26

SP - 68

EP - 77

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

SN - 0963-5483

IS - 1

ER -