论文标题
部分可观测时空混沌系统的无模型预测
Online Ramsey numbers of ordered paths and cycles
论文作者
论文摘要
有序图是其顶点上有线性排序的图。在线Ramsey游戏订购的图形$ G $和$ H $是在无限序列上播放的；在每个回合中，建筑商都在两个顶点之间绘制一个边缘，而画家则将其颜色为红色或蓝色。建筑商试图尽快创建红色$ g $或蓝色$ h $，而画家则希望相反。在线订购的Ramsey编号$ r_o（g，h）$是游戏持续的转弯数。 在本文中，我们考虑了$ r_o（g，p_n）$的行为，$ g $，其中$ p_n $是单调订购路径。我们证明了$ o（n \ log_2n）$在$ r_o（g，p_n）$上绑定了所有$ g $，而当$ g $为$ 3 $ 3 $ -ICHROACT时，$ o（n）$绑定了；我们将$ r_o（g，p_n）= n + o（1）$进行部分分类$ g $。其中许多结果扩展到$ r_o（g，c_n）$，其中$ c_n $是通过添加一个边缘从$ p_n $获得的有序周期。
An ordered graph is a graph with a linear ordering on its vertices. The online Ramsey game for ordered graphs $G$ and $H$ is played on an infinite sequence of vertices; on each turn, Builder draws an edge between two vertices, and Painter colors it red or blue. Builder tries to create a red $G$ or a blue $H$ as quickly as possible, while Painter wants the opposite. The online ordered Ramsey number $r_o(G,H)$ is the number of turns the game lasts with optimal play. In this paper, we consider the behavior of $r_o(G,P_n)$ for fixed $G$, where $P_n$ is the monotone ordered path. We prove an $O(n \log_2n)$ bound on $r_o(G,P_n)$ for all $G$ and an $O(n)$ bound when $G$ is $3$-ichromatic; we partially classify graphs $G$ with $r_o(G,P_n) = n + O(1)$. Many of these results extend to $r_o(G,C_n)$, where $C_n$ is an ordered cycle obtained from $P_n$ by adding one edge.
