Discussiones Mathematicae Graph Theory 28(2) (2008) 375-378
doi: 10.7151/dmgt.1413

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SOLUTION TO THE PROBLEM OF KUBESA

Mariusz Meszka

Faculty of Applied Mathematics
AGH University of Science and Technology
Mickiewicza 30, 30-059, Kraków, Poland
e-mail: meszka@agh.edu.pl

Abstract

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.

Keywords: tree, T-factorization, degree sequence.

2000 Mathematics Subject Classification: 05C70, 05C05, 05C07.

References

[1] D. Froncek and T. Kovarova, Personal communication, 2004-6.
[2] D. Froncek and M. Kubesa, Problem presented at the Workshop in Krynica 2004, Discuss. Math. Graph Theory 26 (2006) 351.
[3] N.D. Tan, On a problem of Froncek and Kubesa, Australas. J. Combin. 40 (2008) 237-246.

Received 9 January 2008
Revised 11 February 2008
Accepted 11 February 2008