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Let $K_{r_1,\ldots,r_s}$ denote the complete multipartite graph with classsizes $r_1,\ldots,r_s$ and let $K_s$ denote the complete graph of order $s$. In2018, Luo determined the maximum number of $K_s$ in 2-connected graphs with agiven circumference. Recently, Lu, Yuan and Zhang determined the maximum numberof $K_{r_1,r_2}$ in 2-connected graphs with a given circumference, and Wangdetermined the maximum number of $K_s$ or $K_{r_1,1,\ldots,1}$ in graphs withgiven matching number. Motivated by these works, we determine the maximumnumber of $K_{r_1,\ldots,r_s}$ in $2$-connected graphs with given circumferenceand large minimum degree. The maximum number of $K_{r_1,\ldots,r_s}$ in graphswith given matching number and large minimum degree is also given.Consequently, we determine the maximum number of $K_{r_1,\ldots,r_s}$ in graphswith a given circumference or matching number. We also solve the correspondingproblems for graphs with a given detour order.

The maximum number of $K_{r_1,\ldots,r_s}$ in graphs with a given circumference or matching number