论文标题
Turán和Ramsey型的结果不可避免
Turán and Ramsey-type results for unavoidable subgraphs
论文作者
论文摘要
我们在边彩图上研究Turán和Ramsey型问题。如果每个颜色类都包含至少一个$ \ varepsilon $ - 比例的边缘，则称为{\ em $ \ varepsilon $ -balanced}的边缘图形。给定的一个家庭$ \ Mathcal {f} $的边彩图，Ramsey函数$ r（\ Varepsilon，\ Mathcal {f}）$是最小的$ n $，任何$ \ varepsilon $ balboranced $ k_n $都必须包含$ f \ in \ n \ nath futa fut的副本$ \ mathrm {ex}（\ varepsilon，n，\ mathcal {f}）$是$ n $ -vertex $ \ varepsilon $ balanced Graph中的最大边数，它避免了所有$ \ MATHCAL {F} $。在本文中，我们考虑了几类边缘色图的Turán函数，我们表明Ramsey函数是有界度图的线性，并且我们证明了一个定理，该定理在两个参数之间产生了关系。
We study Turán and Ramsey-type problems on edge-colored graphs. An edge-colored graph is called {\em $\varepsilon$-balanced} if each color class contains at least an $\varepsilon$-proportion of its edges. Given a family $\mathcal{F}$ of edge-colored graphs, the Ramsey function $R(\varepsilon, \mathcal{F})$ is the smallest $n$ for which any $\varepsilon$-balanced $K_n$ must contain a copy of an $F\in\mathcal{F}$, and the Turán function $\mathrm{ex}(\varepsilon, n, \mathcal{F})$ is the maximum number of edges in an $n$-vertex $\varepsilon$-balanced graph which avoids all of $\mathcal{F}$. In this paper, we consider this Turán function for several classes of edge-colored graphs, we show that the Ramsey function is linear for bounded degree graphs, and we prove a theorem that gives a relationship between the two parameters.
