A new upper bound for the bipartite Ramsey problem
A new upper bound for the bipartite Ramsey problem
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DOI：
10.1002/jgt.20317
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发表时间：
2008-08
影响因子：
0.9
通讯作者：
D. Conlon
中科院分区：
文献类型：
--
作者：
D. Conlon
我们考虑以下问题：n必须多大保证在整个图形kn的边缘的任何两颜色中，n有一个单色kk，在1970年代后期，欧文表明这已经足够了。 ，对于k大的，n≥2k -1（k - 1） - 1。在这里我们对此有所改进，表明这足以接受$$ {n} \ geq（{1} + {o}（{{{{{ 1}））{2}^{{k}+ {1}}} \; {\ log} \; {k}，$$将日志带到基地2。©2008 Wiley Wendericals，Inc。
We consider the following question: how large does n have to be to guarantee that in any two‐coloring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In the late 1970s, Irving showed that it was sufficient, for k large, that n ≥ 2k − 1 (k − 1) − 1. Here we improve upon this bound, showing that it is sufficient to take $${n} \geq ({1} + {o}({1})) {2}^{{k}+ {1}}\; {\log}\; {k},$$ where the log is taken to the base 2. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 351–356, 2008