论文标题
群集和周期的随机图的不对称拉姆西特性
Asymmetric Ramsey Properties of Random Graphs for Cliques and Cycles
论文作者
论文摘要
我们说$ g \ to（f，h）$如果在每个边缘着色$ c：e（g）\ to \ {1,2 \} $中，我们可以找到$ 1 $ 1 $颜色的$ f $或$ 2 $颜色的副本。众所周知的kohayakawa - kreuter的猜想指出，属性$ g（n，p）\ to（f，h）$等于$ n^{ - 1/m_ {2}（f，h）} $，其中$ n^{ - 1/m_ {2}（f，h）} $，其中$ m_ {2}（f，h）（f，h）$由\ [m_ {2}（f，h）提供\ left \ {\ dfrac {e（j）} {v（j）-2+1/m_2（h）}：j \ subseteq f，e（j）\ ge 1 \ right \}。 \]在本文中，我们显示了每对循环和集团的Kohayakawa-Kreuter猜想的$ 0 $陈述。
We say that $G \to (F,H)$ if, in every edge colouring $c: E(G) \to \{1,2\}$, we can find either a $1$-coloured copy of $F$ or a $2$-coloured copy of $H$. The well-known Kohayakawa--Kreuter conjecture states that the threshold for the property $G(n,p) \to (F,H)$ is equal to $n^{-1/m_{2}(F,H)}$, where $m_{2}(F,H)$ is given by \[ m_{2}(F,H):= \max \left\{\dfrac{e(J)}{v(J)-2+1/m_2(H)} : J \subseteq F, e(J)\ge 1 \right\}. \] In this paper, we show the $0$-statement of the Kohayakawa--Kreuter conjecture for every pair of cycles and cliques.
