The 3-colored Ramsey number of odd cycles
نویسندگان
چکیده
منابع مشابه
The 3-colored Ramsey number of odd cycles
Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph KN contains a monochromatic copy of a graph L. Bondy and Erdős conjectured that for an odd cycle on n vertices Cn, R(Cn, Cn, Cn) = 4n − 3 for n > 3. This is sharp if true. Luczak proved that if n is odd, then R(Cn, Cn, Cn) = 4n+o(n), as n → ∞. We prove here the exact Bondy-Erdős conjecture for...
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Recently we determined the Ramsey Number r(C7, C7, C7) = 25. Let G = (V (G), E(G)) be an undirected finite graph without any loops or multiple edges, where V (G) denotes its vertex set and E(G) its edge set. In the following we will often consider the complete graph Kp on p vertices and the cycle Cp on p vertices. A k−coloring (F1, F2, . . . , Fk) of a graph G is a coloring of the edges of G wi...
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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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In this paper we study multipartite Ramsey numbers for odd cycles. Our main result is the proof of a conjecture of Gyárfás, Sárközy and Schelp [12]. Precisely, let n ≥ 5 be an arbitrary positive odd integer; then in any two-coloring of the edges of the complete 5-partite graph K(n−1)/2,(n−1)/2,(n−1)/2,(n−1)/2,1 there is a monochromatic cycle of length n. keywords: cycles, Ramsey number, Regular...
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We prove that the chromatic Ramsey number of every odd wheel W2k+1, k ≥ 2 is 14. That is, for every odd wheel W2k+1, there exists a 14-chromatic graph F such that when the edges of F are two-coloured, there is a monochromatic copy of W2k+1 in F , and no graph F with chromatic number 13 has the same property. We ask whether a natural extension of odd wheels to the family of generalized Mycielski...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2005
ISSN: 1571-0653
DOI: 10.1016/j.endm.2005.05.053