The Distribution of Ramsey Numbers
Lane Clark, Frank Gaitan
TL;DR
This paper establishes the asymptotic distribution of non-trivial Ramsey numbers, showing their count up to x grows roughly as the square root of x times the square root of the logarithm of x.
Contribution
It provides the first asymptotic estimate for the distribution of non-trivial Ramsey numbers across integers.
Findings
Number of non-trivial Ramsey numbers up to x is approximately (x ln x)^{1/2}.
The distribution follows a specific order of magnitude.
The result advances understanding of the density of Ramsey numbers.
Abstract
We prove that the number of integers in the interval [0,x] that are non-trivial Ramsey numbers r(k,n) (3 <= k <= n) has order of magnitude (x ln x)**(1/2).
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms