Monochromatic paths in random tournaments

Matija Bucić; Shoham Letzter; Benny Sudakov

doi:10.1002/rsa.20780

Monochromatic paths in random tournaments

Matija Bucić
, Shoham Letzter
, Benny Sudakov

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

10 Scopus citations

Abstract

We prove that, with high probability, any 2-edge-coloring of a random tournament on n vertices contains a monochromatic path of length Ω(n/√logn). This resolves a conjecture of Ben-Eliezer, Krivelevich, and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

Original language	English (US)
Pages (from-to)	69-81
Number of pages	13
Journal	Random Structures and Algorithms
Volume	54
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20780
State	Published - Jan 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

Keywords

Ramsey theory
monochromatic directed path
monochromatic oriented path
size Ramsey number

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10.1002/rsa.20780

Cite this

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title = "Monochromatic paths in random tournaments",

abstract = "We prove that, with high probability, any 2-edge-coloring of a random tournament on n vertices contains a monochromatic path of length Ω(n/√logn). This resolves a conjecture of Ben-Eliezer, Krivelevich, and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.",

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AU - Letzter, Shoham

AU - Sudakov, Benny

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AB - We prove that, with high probability, any 2-edge-coloring of a random tournament on n vertices contains a monochromatic path of length Ω(n/√logn). This resolves a conjecture of Ben-Eliezer, Krivelevich, and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

KW - Ramsey theory

KW - monochromatic directed path

KW - monochromatic oriented path

KW - size Ramsey number

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UR - https://www.scopus.com/pages/publications/85044941366#tab=citedBy

U2 - 10.1002/rsa.20780

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M3 - Article

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JO - Random Structures and Algorithms

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Monochromatic paths in random tournaments

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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