منابع مشابه
On the Ramsey number R(3, 6)
The lower bound for the classical Ramsey number R(4, 6) is improved from 35 to 36. The author has found 37 new edge colorings of K35 that have no complete graphs of order 4 in the first color, and no complete graphs of order 6 in the second color. The most symmetric of the colorings has an automorphism group of order 4, with one fixed point, and is presented in detail. The colorings were found ...
متن کاملThe 3-colored Ramsey number for a 3-uniform loose path of length 3
The values of hypergraph 2-color Ramsey numbers for loose cycles and paths have already been determined. The only known value for more than 2 colors is R(C 3 ; 3) = 8, where C 3 3 is a 3-uniform loose cycle of length 3. Here we determine that R(P 3 3 ; 3) = 9, where P 3 3 is a 3-uniform loose path of length 3. Our proof relies on the determination of the Turán number ex3(9;P 3 3 ). We also find...
متن کاملOn the Ramsey Number of Sparse 3-Graphs
We consider a hypergraph generalization of a conjecture of Burr and Erdős concerning the Ramsey number of graphs with bounded degree. It was shown by Chvátal, Rödl, Trotter, and Szemerédi [The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B 34 (1983), no. 3, 239–243] that the Ramsey number R(G) of a graph G of bounded maximum degree is linear in |V (G)|. We derive...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90060-0