一种可为八色和十三色生成Ramsey着色的新方法
A New Method that can Generate Ramsey Colourings for Eight and Thirteen Colours
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中文总结 AI 辅助
本文提出FBF方法，为8色和13色完全图边着色生成Ramsey着色，并构造了与已有着色非同构的新着色。
中文摘要 AI 辅助
我们研究了与完全图的某些边着色相对应的关系代数的表示。此前，对于颜色数$n$不超过$2000$的情况，已经获得了合适的着色，但有两个例外：$n=8$和$n=13$。使用我们称之为FBF（融合优美融合）方法的方法，我们找到了8色和13色的着色。我们的方法是一种新的猜测-检查方法，我们将其描述为对Comer有限域方法的改编。利用FBF，我们构造了与已发表的5、6、7、9、10、11和12色着色非同构的新着色。
英文摘要
We study representations for relation algebras corresponding to certain edge colourings of complete graphs. Previously suitable colourings were obtained for the number of colours $n$ up to $2000$, with two exceptions: $n = 8$ and $n = 13$. Using a method that we have called the FBF (Fusion Beautiful Fusions) method, we find colourings for $8$ and $13$ colours. Our method is a new guess-and-check approach that we describe as an adaptation of Comer's finite-field method. Using FBF we construct novel colourings that are non-isomorphic to existing published colourings for 5, 6, 7, 9, 10, 11 and 12 colours.
