Estimating multicolor ordered Ramsey numbers

Martin Balko; Klára Grinerová

doi:10.1016/j.disc.2026.115286

Estimating multicolor ordered Ramsey numbers

Martin Balko
, Klára Grinerová

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

Abstract

We study multicolor ordered Ramsey numbers, an analog of the classical Ramsey numbers for an arbitrary number of colors and graphs with linearly ordered vertex sets. We generalize upper and lower bounds on two-colored ordered Ramsey numbers of ordered matchings by Conlon, Fox, Lee, and Sudakov to an arbitrary number of colors. Using the extremal theory of matrices, we prove that the q -color ordered Ramsey numbers of ordered matchings on n vertices with interval chromatic number two are in n^Θ(q), which is tight up to a constant in the exponent. We extend this result to ordered graphs with bounded degeneracy and with interval chromatic number two.

Original language	English
Article number	115286
Journal	Discrete Mathematics
Volume	349
Issue number	11
DOIs	https://doi.org/10.1016/j.disc.2026.115286
State	Published - 1 Nov 2026
Externally published	Yes

Keywords

Ordered Rumsey number
Ordered graph
Ramsey number

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2026.115286

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title = "Estimating multicolor ordered Ramsey numbers",

abstract = "We study multicolor ordered Ramsey numbers, an analog of the classical Ramsey numbers for an arbitrary number of colors and graphs with linearly ordered vertex sets. We generalize upper and lower bounds on two-colored ordered Ramsey numbers of ordered matchings by Conlon, Fox, Lee, and Sudakov to an arbitrary number of colors. Using the extremal theory of matrices, we prove that the q -color ordered Ramsey numbers of ordered matchings on n vertices with interval chromatic number two are in nΘ(q), which is tight up to a constant in the exponent. We extend this result to ordered graphs with bounded degeneracy and with interval chromatic number two.",

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AU - Grinerová, Klára

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N2 - We study multicolor ordered Ramsey numbers, an analog of the classical Ramsey numbers for an arbitrary number of colors and graphs with linearly ordered vertex sets. We generalize upper and lower bounds on two-colored ordered Ramsey numbers of ordered matchings by Conlon, Fox, Lee, and Sudakov to an arbitrary number of colors. Using the extremal theory of matrices, we prove that the q -color ordered Ramsey numbers of ordered matchings on n vertices with interval chromatic number two are in nΘ(q), which is tight up to a constant in the exponent. We extend this result to ordered graphs with bounded degeneracy and with interval chromatic number two.

AB - We study multicolor ordered Ramsey numbers, an analog of the classical Ramsey numbers for an arbitrary number of colors and graphs with linearly ordered vertex sets. We generalize upper and lower bounds on two-colored ordered Ramsey numbers of ordered matchings by Conlon, Fox, Lee, and Sudakov to an arbitrary number of colors. Using the extremal theory of matrices, we prove that the q -color ordered Ramsey numbers of ordered matchings on n vertices with interval chromatic number two are in nΘ(q), which is tight up to a constant in the exponent. We extend this result to ordered graphs with bounded degeneracy and with interval chromatic number two.

KW - Ordered Rumsey number

KW - Ordered graph

KW - Ramsey number

UR - https://www.scopus.com/pages/publications/105042546573

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DO - 10.1016/j.disc.2026.115286

M3 - Article

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VL - 349

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 11

M1 - 115286

ER -

Estimating multicolor ordered Ramsey numbers

Abstract

Keywords

ASJC Scopus subject areas

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