The (t−1)-chromatic Ramsey number for paths

Matija Bucić; Amir Khamseh

doi:10.1002/jgt.22898

The (t−1)-chromatic Ramsey number for paths

Matija Bucić
, Amir Khamseh

Mathematics

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

4 Scopus citations

Abstract

The following relaxation of the classical problem of determining the Ramsey number of a fixed graph has first been proposed by Erdős, Hajnal and Rado over 50 years ago. Given a graph (Formula presented.) and an integer (Formula presented.) determine the minimum number (Formula presented.) such that in any (Formula presented.) -coloured complete graph on (Formula presented.) vertices there is a copy of (Formula presented.) using only edges of some (Formula presented.) colours. We determine the answer precisely when (Formula presented.) is a path.

Original language	English (US)
Pages (from-to)	784-796
Number of pages	13
Journal	Journal of Graph Theory
Volume	102
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22898
State	Published - Apr 2023

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

(t−1)-chromatic Ramsey numbers
Ramsey numbers
edge colouring

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10.1002/jgt.22898

Cite this

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abstract = "The following relaxation of the classical problem of determining the Ramsey number of a fixed graph has first been proposed by Erd{\H o}s, Hajnal and Rado over 50 years ago. Given a graph (Formula presented.) and an integer (Formula presented.) determine the minimum number (Formula presented.) such that in any (Formula presented.) -coloured complete graph on (Formula presented.) vertices there is a copy of (Formula presented.) using only edges of some (Formula presented.) colours. We determine the answer precisely when (Formula presented.) is a path.",

keywords = "(t−1)-chromatic Ramsey numbers, Ramsey numbers, edge colouring",

author = "Matija Buci{\'c} and Amir Khamseh",

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year = "2023",

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AU - Khamseh, Amir

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AB - The following relaxation of the classical problem of determining the Ramsey number of a fixed graph has first been proposed by Erdős, Hajnal and Rado over 50 years ago. Given a graph (Formula presented.) and an integer (Formula presented.) determine the minimum number (Formula presented.) such that in any (Formula presented.) -coloured complete graph on (Formula presented.) vertices there is a copy of (Formula presented.) using only edges of some (Formula presented.) colours. We determine the answer precisely when (Formula presented.) is a path.

KW - (t−1)-chromatic Ramsey numbers

KW - Ramsey numbers

KW - edge colouring

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JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 4

ER -

The (t−1)-chromatic Ramsey number for paths

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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