Geodesic
Solution to the problem of Kubesa
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 375-378.

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An infinite family of T-factorizations of complete graphs K_2n, 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 
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Meszka, Mariusz. Solution to the problem of Kubesa. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 375-378. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a12/

[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.