Ramsey numbers of stars versus wheels of similar sizes

Aleksandra Korolova

doi:10.1016/j.disc.2004.12.003

Ramsey numbers of stars versus wheels of similar sizes

Aleksandra Korolova

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

7 Scopus citations

Abstract

We study the Ramsey number R(Wm,Sn) for a star Sn on n vertices and a wheel Wm on m+1 vertices. We show that the Ramsey number R(Wm,Sn)=3n-2 for n=m,m+1, and m+2, where m≥7 and odd. In addition, we give the following lower bound for R(Wm,Sn) where m is even: R(Wm,Sn)≥2n+1 for all n≥m≥6.

Original language	English (US)
Pages (from-to)	107-117
Number of pages	11
Journal	Discrete Mathematics
Volume	292
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.12.003
State	Published - Mar 28 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Keywords

Ramsey number
Star
Wheel

Access to Document

10.1016/j.disc.2004.12.003

Cite this

@article{3b7dae7fd0d44b15bcc6fb4d743e1bf9,

title = "Ramsey numbers of stars versus wheels of similar sizes",

abstract = "We study the Ramsey number R(Wm,Sn) for a star Sn on n vertices and a wheel Wm on m+1 vertices. We show that the Ramsey number R(Wm,Sn)=3n-2 for n=m,m+1, and m+2, where m≥7 and odd. In addition, we give the following lower bound for R(Wm,Sn) where m is even: R(Wm,Sn)≥2n+1 for all n≥m≥6.",

keywords = "Ramsey number, Star, Wheel",

author = "Aleksandra Korolova",

note = "Funding Information: This research was performed under the supervision of Prof. Joseph Gallian at the University of Minnesota Duluth. The work was supported by NSF Grant DMS-0137611. The author would like to thank Prof. Gallian for organizing his excellent REU Program and for his guidance and support throughout the program. In addition, the author would like to thank Geir Helleloid and Philip Matchett for their helpful comments on the manuscript. The author would also like to thank Maksim Maydanskiy, another participant in the REU, for his suggestions on how to approach the problem. ",

year = "2005",

month = mar,

day = "28",

doi = "10.1016/j.disc.2004.12.003",

language = "English (US)",

volume = "292",

pages = "107--117",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "1-3",

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TY - JOUR

T1 - Ramsey numbers of stars versus wheels of similar sizes

AU - Korolova, Aleksandra

N1 - Funding Information: This research was performed under the supervision of Prof. Joseph Gallian at the University of Minnesota Duluth. The work was supported by NSF Grant DMS-0137611. The author would like to thank Prof. Gallian for organizing his excellent REU Program and for his guidance and support throughout the program. In addition, the author would like to thank Geir Helleloid and Philip Matchett for their helpful comments on the manuscript. The author would also like to thank Maksim Maydanskiy, another participant in the REU, for his suggestions on how to approach the problem.

PY - 2005/3/28

Y1 - 2005/3/28

N2 - We study the Ramsey number R(Wm,Sn) for a star Sn on n vertices and a wheel Wm on m+1 vertices. We show that the Ramsey number R(Wm,Sn)=3n-2 for n=m,m+1, and m+2, where m≥7 and odd. In addition, we give the following lower bound for R(Wm,Sn) where m is even: R(Wm,Sn)≥2n+1 for all n≥m≥6.

AB - We study the Ramsey number R(Wm,Sn) for a star Sn on n vertices and a wheel Wm on m+1 vertices. We show that the Ramsey number R(Wm,Sn)=3n-2 for n=m,m+1, and m+2, where m≥7 and odd. In addition, we give the following lower bound for R(Wm,Sn) where m is even: R(Wm,Sn)≥2n+1 for all n≥m≥6.

KW - Ramsey number

KW - Star

KW - Wheel

UR - https://www.scopus.com/pages/publications/15344349167

UR - https://www.scopus.com/pages/publications/15344349167#tab=citedBy

U2 - 10.1016/j.disc.2004.12.003

DO - 10.1016/j.disc.2004.12.003

M3 - Article

AN - SCOPUS:15344349167

SN - 0012-365X

VL - 292

SP - 107

EP - 117

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

Ramsey numbers of stars versus wheels of similar sizes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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