Geodesic
A Note on the Ramsey Number of Even Wheels Versus Stars
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 397-404

Voir la notice de l'article provenant de la source Library of Science

For two graphs G_1 and G_2, the Ramsey number R(G_1,G_2) is the smallest integer N, such that for any graph on N vertices, either G contains G_1 or G contains G_2. Let S_n be a star of order n and W_m be a wheel of order m + 1. In this paper, we will show R(W_n, S_n) ≤ 5n//2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(W_n, S_n) = 5n//2 − 2 or 5n//2 −1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(W_n, S_n) = 5n//2 − 2.
Keywords: Ramsey number, star, wheel, weakly pancyclic 
@article{DMGT_2018_38_2_a4,
     author = {Haghi, Sh. and Maimani, H.R.},
     title = {A {Note} on the {Ramsey} {Number} of {Even} {Wheels} {Versus} {Stars}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {397--404},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a4/}
}
TY  - JOUR
AU  - Haghi, Sh.
AU  - Maimani, H.R.
TI  - A Note on the Ramsey Number of Even Wheels Versus Stars
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2018
SP  - 397
EP  - 404
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a4/
LA  - en
ID  - DMGT_2018_38_2_a4
ER  - 
%0 Journal Article
%A Haghi, Sh.
%A Maimani, H.R.
%T A Note on the Ramsey Number of Even Wheels Versus Stars
%J Discussiones Mathematicae. Graph Theory
%D 2018
%P 397-404
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a4/
%G en
%F DMGT_2018_38_2_a4
Haghi, Sh.; Maimani, H.R. A Note on the Ramsey Number of Even Wheels Versus Stars. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 397-404. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a4/