论文标题
部分可观测时空混沌系统的无模型预测
The Ramsey Number for a Forest versus Disjoint Union of Complete Graphs
论文作者
论文摘要
给定两个图$ g $和$ h $，Ramsey数字$ r（g，h）$是最小整数$ n $，因此，红色或蓝色的$ k_n $的任何颜色都会产生红色$ g $或蓝色$ h $。令$ v（g）$为$ g $的顶点，$χ（g）$是$ g $的色数。令$ s（g）$表示$ g $的色彩盈余，这是所有$ g $的最低颜色类的基数，$χ$，$χ（g）$颜色。伯尔（Burr）表明，对于连接的图形$ g $和图$ h $，带有$ v（g）\ geq s（h）$，$ r（g，h）\ geq（v（g）-1）（χ（H）-1 -1）+s（h）$。如果$ r（g，h）=（v（g）-1）（χ（H）-1）-1）+S（H）$，则称为$ H $ -OGOD $ H $ -OGOD。在本文中，我们主要确认任何树$ t_n $对$ k_m \ cup k_l $的Ramsey号码。我们的结果产生的是$ t_n $是$ k_m \ cup k_l $ -ogood。
Given two graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum integer $N$ such that any coloring of the edges of $K_N$ in red or blue yields a red $G$ or a blue $H$. Let $v(G)$ be the number of vertices of $G$ and $χ(G)$ be the chromatic number of $G$. Let $s(G)$ denote the chromatic surplus of $G$, the cardinality of a minimum color class taken over all proper colorings of $G$ with $χ(G)$ colors. Burr showed that for a connected graph $G$ and a graph $H$ with $v(G)\geq s(H)$, $R(G,H) \geq (v(G)-1)(χ(H)-1)+s(H)$. A connected graph $G$ is called $H$-good if $R(G,H)=(v(G)-1)(χ(H)-1)+s(H)$. In this paper, we mainly confirm the Ramsey number for any tree $T_n$ versus $K_m\cup K_l$. Our result yields that $T_n$ is $K_m\cup K_l$-good.
