Solution to the problem of Kubesa

An infinite family of T-factorizations of complete graphs ${\displaystyle K_{2n}}$, where 2n = 56k and k is a positive integer, in which the set of vertices of T can be split into two subsets of the same cardinality such that degree sums of vertices in both subsets are not equal, is presented. The existence of such T-factorizations provides a negative answer to the problem posed by Kubesa.