论文标题
$ k_ {r_1，\ ldots，r_s} $的最大数量，带有给定的圆周或匹配号码
The maximum number of $K_{r_1,\ldots,r_s}$ in graphs with a given circumference or matching number
论文作者
论文摘要
令$ k_ {r_1，\ ldots，r_s} $表示具有类尺寸$ r_1，\ ldots，r_s $的完整多明位图，然后$ k_s $表示订单$ s $的完整图。在2018年，Luo确定了具有给定圆周的2个连接图中的$ k_s $的最大数量。最近，Lu，Yuan和Zhang确定了具有给定圆周的2个连接图中的$ k_ {r_1，r_2} $的最大数量，Wang确定了具有给定匹配数的图中的最大$ k_s $或$ k_s $或$ k_ {r_1,1，\ ldots，\ ldots，1} $。由这些作品激励，我们确定$ k_ {r_1，\ ldots，r_s} $的最大数量，$ 2 $连接的图形具有给定的圆周和大最低度。还给出了$ k_ {r_1，\ ldots，r_s} $的最大数量，并给定给定的匹配数和最小的最低度。因此，我们确定具有给定圆周或匹配数字的图形中$ k_ {r_1，\ ldots，r_s} $的最大数量。我们还解决了具有给定弯路顺序的图形的相应问题。
Let $K_{r_1,\ldots,r_s}$ denote the complete multipartite graph with class sizes $r_1,\ldots,r_s$ and let $K_s$ denote the complete graph of order $s$. In 2018, Luo determined the maximum number of $K_s$ in 2-connected graphs with a given circumference. Recently, Lu, Yuan and Zhang determined the maximum number of $K_{r_1,r_2}$ in 2-connected graphs with a given circumference, and Wang determined the maximum number of $K_s$ or $K_{r_1,1,\ldots,1}$ in graphs with given matching number. Motivated by these works, we determine the maximum number of $K_{r_1,\ldots,r_s}$ in $2$-connected graphs with given circumference and large minimum degree. The maximum number of $K_{r_1,\ldots,r_s}$ in graphs with given matching number and large minimum degree is also given. Consequently, we determine the maximum number of $K_{r_1,\ldots,r_s}$ in graphs with a given circumference or matching number. We also solve the corresponding problems for graphs with a given detour order.
