The Ramsey number for a triple of long even cycles
نویسندگان
چکیده
منابع مشابه
The 3-colored Ramsey number of even cycles
Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdős conjectured that when L is the cycle Cn on n vertices, R(Cn, Cn, Cn) = 4n − 3 for every odd n > 3. Luczak proved that if n is odd, then R(Cn, Cn, Cn) = 4n + o(n), as n → ∞, and Kohayakawa, Simonovits and Skokan confirmed...
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Let H s − → G denote that any s-coloring of E(H) contains a monochromatic G. The degree Ramsey number of a graph G, denoted by R∆(G, s), is min{∆(H) : H s − → G}. We consider degree Ramsey numbers where G is a fixed even cycle. Kinnersley, Milans, and West showed that R∆(C2k, s) ≥ 2s, and Kang and Perarnau showed that R∆(C4, s) = Θ(s 2). Our main result is that R∆(C6, s) = Θ(s 3/2) and R∆(C10, ...
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For given finite family of graphs G1, G2, . . . , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, . . . , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of Gi colored with i, for some 1 ≤ i ≤ k. We give a lower bound for k−color Ramsey number R(Cm, Cm, . . . , Cm), where m ≥ ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.09.001