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...
متن کاملThe 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...
متن کامل3-colored Ramsey Numbers of Odd Cycles
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...
متن کاملOn the Multi-Colored Ramsey Numbers of Paths and Even Cycles
In this paper we improve the upper bound on the multi-color Ramsey numbers of paths and even cycles.
متن کاملCanonical Ramsey numbers and properly colored cycles
We improve the previous bounds on the so-called unordered Canonical Ramsey numbers, introduced by Richer [D. Richer, Unordered canonical Ramsey numbers, Journal of Combinatorial Theory Series B 80 (2000) 172–177] as a variant of the canonical Ramsey numbers introduced by Erdős and Rado [P. Erdős, R. Rado, A combinatorial theorem, Journal of the London Mathematical Society 25 (4) (1950) 249–255]...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2009
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2008.12.002