论文标题
Ramsey Number $ r（5,5）$的Exoo的下限
Study of Exoo's Lower Bound for Ramsey number $R(5,5)$
论文作者
论文摘要
我们回顾了Exoo的1989年论文，该论文表明Ramsey Number $ r（5,5）$的下限为$ 43 $。我们提供了一种有效的方法来验证论文中的索赔，并增加了详细的证明。特别是，我们通过简洁的参数替换对计算机验证的引用。利用我们对这些证据背后的见解的理解，我们还能够分析图形构造的变化，例如获得$ k_ {43} $的颜色，这些颜色很少有单色$ k_5 $。
We review Exoo's 1989 paper, which demonstrates that a lower bound for the Ramsey number $R(5,5)$ is $43$. We provide an efficient way to verify the claims in the paper, adding detailed proofs. In particular, we replace the reference to computer verification by concise arguments. Using our understanding of the insight behind these proofs, we are also able to analyse variations of the graph constructions to obtain, for example, colourings of $K_{43}$ which have very few monochromatic $K_5$.
