2018
Том 70
№ 9

All Issues

Petrenyuk A. Ya.

Articles: 5
Article (Ukrainian)

Nonexistence of some T-factorizations of order 12

Petrenyuk A. Ya.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

On Bicyclic T-Factorizability in the Class T[14, 6]

Petrenyuk A. Ya.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Semirotational Tree Factorizations of Complete Graphs

Petrenyuk A. Ya.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Tests for nonisomorphic Steiner triple systems

Petrenyuk A. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 6. - pp. 772—780

Article (Ukrainian)

Towards the proof of a theorem of Grünbaum

Petrenyuk A. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 268–269