论文标题
turán密度为$ 2 $ - 边缘色的两分图，并在$ \ {2，3 \} $上使用应用
Turán Density of $2$-edge-colored Bipartite Graphs with Application on $\{2, 3\}$-Hypergraphs
论文作者
论文摘要
我们认为Turán的问题是$ 2 $ - 边缘色的图。 $ 2 $ - 边缘色的图$ h =（v，e_r，e_b）$是由顶点套装$ v $，一组红色边缘$ e_r $的三重组成的三重组，以及一组蓝色边缘$ e_b $，带有$ e_r $和$ e_b $的$ E_B $，不必是分离的。 $ h $的turán密度$π（h）$定义为$ \ lim_ {n \ to \ infty} \ max_ {g_n} h_n（g_n）$，其中$ g_n $在所有可能的$ 2 $ edg $ n $ fertices中选择了$ n $ note $ n $ n $ h $ h $ h $ h $ s selp selp and s s selp-h $ $ h_n（g_n）=（| e_r（g）|+| e_b（g）|）/{n \ select 2} $是测量$ g_n $的边缘密度的公式。我们将确定所有$ 2 $ - 边缘色的两部分图的Turán密度。我们还对$ \ {2，3 \} $ - 超图的Turán问题进行了重要的研究。
We consider the Turán problems of $2$-edge-colored graphs. A $2$-edge-colored graph $H=(V, E_r, E_b)$ is a triple consisting of the vertex set $V$, the set of red edges $E_r$ and the set of blue edges $E_b$ with $E_r$ and $E_b$ do not have to be disjoint. The Turán density $π(H)$ of $H$ is defined to be $\lim_{n\to\infty} \max_{G_n}h_n(G_n)$, where $G_n$ is chosen among all possible $2$-edge-colored graphs on $n$ vertices containing no $H$ as a sub-graph and $h_n(G_n)=(|E_r(G)|+|E_b(G)|)/{n\choose 2}$ is the formula to measure the edge density of $G_n$. We will determine the Turán densities of all $2$-edge-colored bipartite graphs. We also give an important application of our study on the Turán problems of $\{2, 3\}$-hypergraphs.
