论文标题
定向拉姆齐号r（7）上的更紧密的界限
Tighter Bounds on Directed Ramsey Number R(7)
论文作者
论文摘要
锦标赛是完整图的方向，而定向的Ramsey Number $ r（k）$是必须保证必须保证比赛的最小顶点数量，以包含$ k $的瞬时子比赛，我们用$ tt_k $表示。我们包括桑切斯 - 弗洛雷斯（Sanchez-Flores）猜想的计算机辅助证明，即24和25个顶点上的所有$ tt_6 $ free锦标赛都是$ st_ {27} $的亚顾问，这是独特的最大TT_6无tt_6的无tt_6免费锦标赛。我们还对23个顶点上的所有$ tt_6 $ free比赛进行了分类。我们使用这些结果，再加上SAT技术的帮助，以获得以下改进的界限：$ 34 \ leq r（7）\ leq 47 $。
Tournaments are orientations of the complete graph, and the directed Ramsey number $R(k)$ is the minimum number of vertices a tournament must have to be guaranteed to contain a transitive subtournament of size $k$, which we denote by $TT_k$. We include a computer-assisted proof of a conjecture by Sanchez-Flores that all $TT_6$-free tournaments on 24 and 25 vertices are subtournaments of $ST_{27}$, the unique largest TT_6-free tournament. We also classify all $TT_6$-free tournaments on 23 vertices. We use these results, combined with assistance from SAT technology, to obtain the following improved bounds: $34 \leq R(7) \leq 47$.
