the ramsey numbers of large trees versus wheels
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for two given graphs g1 and g2, the ramseynumber r(g1,g2) is the smallest integer n such that for anygraph g of order n, either $g$ contains g1 or the complementof g contains g2. let tn denote a tree of order n andwm a wheel of order m+1. to the best of our knowledge, only r(tn,wm) with small wheels are known.in this paper, we show that r(tn,wm)=3n-2 for odd m with n>756m^{10}.
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For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۴، صفحات ۸۷۹-۸۸۰
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