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Solution to the problem of Kubesa

An infinite family of T -factorizations of complete graphs K2n, 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.