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
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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 -