C5 ${C}_{5}$ is almost a fractalizer
C5 ${C}_{5}$ is almost a fractalizer
复制标题
C5 ${C}_{5}$ 几乎是一个分形器
DOI：
10.1002/jgt.22957
复制
发表时间：
2023
影响因子：
0.9
通讯作者：
Pfender, Florian
中科院分区：
文献类型：
--
作者：
Lidický, Bernard;Mattes, Connor;Pfender, Florian
我们确定了图中n$n$个顶点上的5-圈的最大诱导拷贝数。每个极值构造都是5圈的平衡迭代爆破，可能的例外是最小水平，其中对于n=8$n=8$，Möbius阶梯达到与8个顶点上的5圈爆破相同的诱导5圈的数目。这一结果完成了巴洛赫、胡、李迪克和普芬德的工作，他们证明了结果的渐近版本。与他们的结果类似，我们也使用了旗帜代数方法，但我们使用了一种新的、更复杂的方法，允许我们将其扩展到小图。
We determine the maximum number of induced copies of a 5‐cycle in a graph on n $n$ vertices for every n $n$. Every extremal construction is a balanced iterated blow‐up of the 5‐cycle with the possible exception of the smallest level where for n = 8 $n=8$, the Möbius ladder achieves the same number of induced 5‐cycles as the blow‐up of a 5‐cycle on eight vertices. This result completes the work of Balogh, Hu, Lidický, and Pfender, who proved an asymptotic version of the result. Similarly to their result, we also use the flag algebra method, but we use a new and more sophisticated approach which allows us to extend its use to small graphs.