  We present several criteria for genuine multipartite entanglement from
universal uncertainty relations based on majorization theory. Under
non-negative Schur-concave functions, the vector-type uncertainty relation
generates a family of infinitely many detectors to check genuine multipartite
entanglement. We also introduce the concept of $k$-separable circles via
geometric distance for probability vectors, which include at most
$(k-1)$-separable states. The entanglement witness is also generalized to a
universal entanglement witness which is able to detect the $k$-separable states
more accurately.
