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

2 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

Access to Document

10.1002/jgt.22898

Cite this

@article{e407a1be38d449a7a6551964961af013,

title = "The (t−1)-chromatic Ramsey number for paths",

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",

note = "Publisher Copyright: {\textcopyright} 2022 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.",

year = "2023",

month = apr,

doi = "10.1002/jgt.22898",

language = "English (US)",

volume = "102",

pages = "784--796",

journal = "Journal of Graph Theory",

issn = "0364-9024",

publisher = "Wiley-Liss Inc.",

number = "4",

}

TY - JOUR

T1 - The (t−1)-chromatic Ramsey number for paths

AU - Bucić, Matija

AU - Khamseh, Amir

PY - 2023/4

Y1 - 2023/4

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85140120180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85140120180&partnerID=8YFLogxK

U2 - 10.1002/jgt.22898

DO - 10.1002/jgt.22898

M3 - Article

AN - SCOPUS:85140120180

SN - 0364-9024

VL - 102

SP - 784

EP - 796

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

Access to Document

Other files and links

Fingerprint

Cite this