论文标题
带有较低方向的Ramsey阈值的定向图
Directed graphs with lower orientation Ramsey thresholds
论文作者
论文摘要
我们研究了Ramsey-type属性$ g（n，p）\ to \ vec h $，其中$ g（n，p）$是binmial andomial gromang grangage and $ g \ v \ vec h $ the $ g \ the Gragraute $ g \ the $ g \ the Gragrauth $ g \ the Gragraute $ g \ the Gragraute $ g \ the Gragrauth $ g \ the Gragrauth $ g \， h $作为子数字。 Similarly to the classical Ramsey setting, the upper bound $p_{\vec H}\leq Cn^{-1/m_2(\vec H)}$ is known to hold for some constant $C=C(\vec H)$, where $m_2(\vec H)$ denotes the maximum $2$-density of the underlying graph $H$ of $\vec H$.尽管这种上限确实是一些$ \ vec h $的门槛，但并非总是如此。我们获得了稀疏图（例如森林，周期和更一般而言的亚地下$ \ {k_3，k_3，k_ {3,3} \} $ - 免费图）和任意根生根的三角形三角形的稀疏图（例如森林，周期和更一般而言）产生的示例。
We investigate the threshold $p_{\vec H}=p_{\vec H}(n)$ for the Ramsey-type property $G(n,p)\to \vec H$, where $G(n,p)$ is the binomial random graph and $G\to\vec H$ indicates that every orientation of the graph $G$ contains the oriented graph $\vec H$ as a subdigraph. Similarly to the classical Ramsey setting, the upper bound $p_{\vec H}\leq Cn^{-1/m_2(\vec H)}$ is known to hold for some constant $C=C(\vec H)$, where $m_2(\vec H)$ denotes the maximum $2$-density of the underlying graph $H$ of $\vec H$. While this upper bound is indeed the threshold for some $\vec H$, this is not always the case. We obtain examples arising from rooted products of orientations of sparse graphs (such as forests, cycles and, more generally, subcubic $\{K_3,K_{3,3}\}$-free graphs) and arbitrarily rooted transitive triangles.
