论文标题
在弱的图形上
On weakly Turán-good graphs
论文作者
论文摘要
给定图形$ h $和$ f $带有$χ（h）<χ（f）$，我们说$ h $是$ h $ $ f $-turán-good如果在$ n $ n $ -vertex $ f $ - f $ - f $ - f $ - a $（χ（f）-1）$ - partite图中包含最多副本$ h $。令$ h $是一个包含完整的两部分子图$ k $的两部分图，以便每个顶点$ h $都与$ k $的顶点相邻。我们表明，$ h $是$ k_3 $-turán-good，由于Grzesik，gy \ h ori，Salia和Tompkins，改善了最近的渐近线。他们还表明，对于任何$ r $，存在并不是微弱$ k_r $-turán-good的图。我们表明，对于任何非双方$ f $，存在并非弱$ f $-turán-good的图表。我们还显示了$ c_ {2k+1} $ - turán-good的图表示例，但不为$ c_ {2 \ ell+1} $-Turán-good，每$ k> \ ell $。
Given graphs $H$ and $F$ with $χ(H)<χ(F)$, we say that $H$ is weakly $F$-Turán-good if among $n$-vertex $F$-free graphs, a $(χ(F)-1)$-partite graph contains the most copies of $H$. Let $H$ be a bipartite graph that contains a complete bipartite subgraph $K$ such that each vertex of $H$ is adjacent to a vertex of $K$. We show that $H$ is weakly $K_3$-Turán-good, improving a very recent asymptotic bound due to Grzesik, Gy\H ori, Salia and Tompkins. They also showed that for any $r$ there exist graphs that are not weakly $K_r$-Turán-good. We show that for any non-bipartite $F$ there exists graphs that are not weakly $F$-Turán-good. We also show examples of graphs that are $C_{2k+1}$-Turán-good but not $C_{2\ell+1}$-Turán-good for every $k>\ell$.
