.1 Results
نویسنده
چکیده
Current Day Annotation These notes were written in 1995. Since 1961 the best lower bound on R(3, k) had been ck2 ln−2 k. Building on a paper of Erdős, Winkler and Suen I was able to show that c could be made arbitrarily large. Why didn’t I publish? Only a few weeks later Jeong-Han Kim found that R(3, k) = Ω(k2 ln−1 k), matching the upper bound of Ajtai, Komlós and Szemerédi, so thatR(3, k) = Θ(k2 ln−1 k). The ideas in these notes, studying the random greedy trianglefree algorithm, were cited by Tom Bohman in his analysis of this process and his alternate proof of Kim’s result.
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تاریخ انتشار 2011