论文标题
部分可观测时空混沌系统的无模型预测
On vertex Ramsey graphs with forbidden subgraphs
论文作者
论文摘要
A classical vertex Ramsey result due to Nešetřil and Rödl states that given a finite family of graphs $\mathcal{F}$, a graph $A$ and a positive integer $r$, if every graph $B\in\mathcal{F}$ has a $2$-vertex-connected subgraph which is not a subgraph of $A$, then there exists an $ \ MATHCAL {F} $ - 免费图形，即$ a $。我们证明，对于存在$ \ Mathcal {f} $的存在这种足够的条件 - 免费图形，即对于$ a $的顶点$ r $ -ramsey，对于大量的大量颜色$ r $也是必需的。 我们进一步显示了结果对图的概括，并且在密集的二项式随机图中典型的这种子图的典型存在。
A classical vertex Ramsey result due to Nešetřil and Rödl states that given a finite family of graphs $\mathcal{F}$, a graph $A$ and a positive integer $r$, if every graph $B\in\mathcal{F}$ has a $2$-vertex-connected subgraph which is not a subgraph of $A$, then there exists an $\mathcal{F}$-free graph which is vertex $r$-Ramsey with respect to $A$. We prove that this sufficient condition for the existence of an $\mathcal{F}$-free graph which is vertex $r$-Ramsey with respect to $A$ is also necessary for large enough number of colours $r$. We further show a generalisation of the result to a family of graphs and the typical existence of such a subgraph in a dense binomial random graph.
