منابع مشابه
Stability of the path-path Ramsey number
Here we prove a stability version of a Ramsey-type Theorem for paths. Thus in any 2-coloring of the edges of the complete graph Kn we can either find a monochromatic path substantially longer than 2n/3, or the coloring is close to the extremal coloring.
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We give a lower bound for the Ramsey number and the planar Ramsey number for C4 and complete graphs. We prove that the Ramsey number for C4 and K7 is 21 or 22. Moreover we prove that the planar Ramsey number for C4 and K6 is equal to 17.
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Let Q(n, χ) denote the minimum clique size an n-vertex graph can have if its chromatic number is χ . Using Ramsey graphs we give an exact, albeit implicit, formula for the case χ ≥ (n + 3)/2.
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The Ramsey number r(H) of a graphH is the smallest number n such that, in any two-colouring of the edges of Kn, there is a monochromatic copy of H . We study the Ramsey number of graphs H with t vertices and density ρ, proving that r(H) ≤ 2 √ ρ . We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree ρt and the Ramsey number of random g...
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Consider the following one-player game. Starting with the empty graph on n vertices, in every step r new edges are drawn uniformly at random and inserted into the current graph. These edges have to be colored immediately with r available colors, subject to the restriction that each color is used for exactly one of these edges. The player’s goal is to avoid creating a monochromatic copy of some ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2015
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548315000279