Genus of complete $ k $-partite graph What is the formula for the genus of a complete $ k $-partite graph, with partite set of size $n_1,n_2,\dots,n_k$, where $ k $ is an integer greater than or equal to $3$?

The complete bipartite graph $K_{m,n}$ has genus $\left\lceil\frac{(m-2)(n-2)}{4}\right\rceil$ (from <

Bettayeb has a paper on the genus of complete multipartite graphs; see Link.