منابع مشابه
An Upper Bound for the Ramsey Numbers
The Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N -vertex complete graph KN in red and blue, it must contain either a red H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3, G) ≤ 2q + 1 where G has q edges. In other words, any graph on 2q + 1 vertices with independence number at most 2 contains every (iso...
متن کاملAn upper bound for the Ramsey numbers r(&, G)*
The Ramsey number r(H, G) is defined as the minimum N such that for any coloring of the edges of the N-vertex complete graph KN in red and blue, it must contain either a ted H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K,, G)< 2qf 1 where G has q edges. In other words, any graph on 2q+ 1 vertices with independence number at most 2 contains every (isolat...
متن کاملNew upper bound formulas with parameters for Ramsey numbers
In this paper, we obtain some new results R(5, 12) 848, R(5, 14) 1461, etc., and we obtain new upper bound formulas for Ramsey numbers with parameters. © 2006 Published by Elsevier B.V.
متن کاملA New Upper Bound for Diagonal Ramsey Numbers
We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant C such that r(k + 1, k + 1) ≤ k log k log log k (
متن کاملAn Upper Bound for Uniform Entropy Numbers
Let r > 1 and let Q be a probability measure on a measurable space (X, .4). In this note, we present a proof of a useful bound in Lr ( Q)-norm for the entropy of a convex hull in the case that covering numbers for a class of measurable functions are polynomial.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1966
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1966-11652-x