Skip to main content
Log in

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

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. L. W. Beineke, “Decomposition of complete graphs into forests,” Magy. Tud. Akad. Kut. Intéz. Közl., 9, 589–594 (1964).

    Google Scholar 

  2. C. Huang and A. Rosa, “Decomposition of complete graphs into trees,” Ars Combinat., 5, 23–63 (1978).

    Google Scholar 

  3. A. J. Petrenjuk, “Enumeration of minimal tree decompositions of complete graphs,” J. Combin. Math. Combin. Computing, 12, 197–199 (1992).

    Google Scholar 

  4. L. P. Petrenyuk, List of Decompositions of Complete Graphs into Isomorphic Components [in Ukrainian], Candidate-Degree Thesis (Physics and Mathematics), Kirovograd (1996).

    Google Scholar 

  5. A. J. Petrenjuk, “On tree factorization of K10,” J. Combin. Math. Combin. Comput., 41, 193–202 (2002).

    Google Scholar 

  6. A. J. Petrenjuk, Every Tree from T [14, 4] Admits a T-Factorization, Deposited in Ukrainian DNTB, No. 147-Uk 2001, Kirovograd (2001).

    Google Scholar 

  7. A. Ya. Petrenyuk, “On the existence of bicyclic T-factorizations of order 14,” in: R. N. Makarov (editor), Proceedings of the Academy [in Russian], Ukrainian State Aviation Academy, Kirovograd, Issue 4, Part 1 (1999), pp. 206–212.

    Google Scholar 

  8. A. Ya. Petrenyuk, “Tree factorizations of complete graphs: the existence, construction, and enumeration,” in: Proceedings of the 7 th International Seminar “Discrete Mathematics and Its Applications” (January - February 2001) [in Russian], Center of Applied Investigations at the Mechanical and Mathematical Department of the Moscow University, Moscow, Part 1 (2001), pp. 26–30.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petrenyuk, A.Y. On Bicyclic T-Factorizability in the Class T[14, 6]. Ukrainian Mathematical Journal 55, 1207–1217 (2003). https://doi.org/10.1023/B:UKMA.0000010617.44846.98

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000010617.44846.98

Keywords

Navigation