论文标题
关于图中三角形数量的注释，而无需在四个顶点上悬挂路径
A note on the number of triangles in graphs without the suspension of a path on four vertices
论文作者
论文摘要
路径$ P_4 $的悬架由$ P_4 $和连接到四个顶点的每个顶点组成，并用$ \ hat {p_4} $表示。 $ \ hat {p_4} $ - 免费$ n $ -vertex图中最大数量的三角形图表示$ ex（n，k_3，\ hat {p_4}）$。 Mubayi和Mukherjee在2020年表明$ ex（n，k_3，\ hat {p_4}）= n^2/8+o（n）$。我们表明，对于足够大的$ n $，$ ex（n，k_3，\ hat {p_4}）= \ lfloor n^2/8 \ rfloor $。
The suspension of the path $P_4$ consists of a $P_4$ and an additional vertex connected to each of the four vertices, and is denoted by $\hat{P_4}$. The largest number of triangles in a $\hat{P_4}$-free $n$-vertex graph is denoted by $ex(n,K_3,\hat{P_4})$. Mubayi and Mukherjee in 2020 showed that $ ex(n,K_3,\hat{P_4})= n^2/8+O(n)$. We show that for sufficiently large $n$, $ex(n,K_3,\hat{P_4})=\lfloor n^2/8\rfloor$.
