Petrenyuk A. Ya.
Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 666–674
We investigate the Beineke problem of the existence of T-factorizations of complete graphs and prove several theorems on the existence of T-factorizations. Using these theorems, we establish the nonexistence of T-factorizations for 32 nonisomorphic admissible trees of order 12.
Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 998-1005
We completely solve the problem of the existence of T-factorizations in the class of trees of order 14 with the largest vertex order 6.
Ukr. Mat. Zh. - 2001. - 53, № 5. - pp. 715-721
We select the class of so-called semisymmetric trees and prove that every tree T from this class admits a T-factorization of a special form in the case where T is of order n = 2k ≤ 16. We formulate the conjecture that every semisymmetric tree T admits a T-factorization. We establish the existence of a T-factorization for semisymmetric trees of certain classes.
Ukr. Mat. Zh. - 1972. - 24, № 6. - pp. 772—780
Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 268–269